5 more than 8 times a number algebraic expression

State at least 5 things in your living room that suggest a point, a line, or a plane. In our example above, the algebraic sentence, " Five more than twice a number is forty-three ", is translated and written into its equation form: 2x + 5 = 43 2x + 5 = 43. In this algebraic sentence, both sides of the equation contain an algebraic expression. In the problem above, x is a variable. 2 diminished by 7 times a number 5. D. All terminating decimals and non-repeating are rational. Direct link to bruh's post Well, if b doesn't have v, Learn to write expressions for phrases like "3 more than x.". Yes, it does! Many teachers in the early math years may not be doing, How to find the surface area of a trapezoidal prism, Converting improper fractions to mixed numbers calculator. You may notice that we translated the difference of 16 and k into an algebraic expression, 16-k, then used the equal symbol (=) in place of the word is. Algebraic expression for 8 more than 5 times a number is 5x+8, In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations, Hence, Algebraic expression for 8 more than 5 times a number is 5x+8, Learn more about Algebraic expression here, This site is using cookies under cookie policy . 4. Algebra Expressions, Equations, and Functions Variable Expressions 1 Answer smendyka Mar 3, 2018 See a solution process below: Explanation: First, let's call "a number": n Next, "twice a number" means to multiply the number by 2 giving: 2 n or 2 n or 2n Then, "five more than" means to add 5 to what follows or: 2n +5 Answer link 2 increased by 5 times a number 6. Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable). 1. Answer link. Direct link to Da'shyne Green's post There should be a timer t, Posted 10 months ago. Find the circumference of the circle using 3 Now, well evaluate the value of \large{x = 4} to verify if the number we found satisfies the original algebraic sentence. They tell us the operation is subtraction. However, for our discussion, we will use 6 + 7x = 34 as our equation. How do you write a quotient of a number and 6 as an expression? Step-by-step explanation: 8 more than 5 times a number. In the following exercises, write an algebraic expression. Well use the variable \large{y} as the placeholder for our number whose value is currently unknown. A 2. Explain the difference between 4 times the sum of x and y and the sum of 4 times x and y., Lynn Marecek (Santa Ana College) andMaryAnne Anthony-Smith (formerly of Santa Ana College). 46829 views How do you evaluate the expression #2x+1# for #x=1#? nine times a number 2.) Writing Algebraic Expressions Step-by-Step Examples. Eric has rock and classical CDs in his car. Look for the words of and and to find the numbers. To organize our thoughts, lets deconstruct this algebraic sentence into its meat and potatoes. 9 decreased by 4 times a number 4 . Example 2: The difference between three times a number and five is sixteen. Eight more than a number is just 8 + n in algebra. Algebra 1 2022-2023. Let n represent the number of nickels. The number of pennies is seven less than twice the number of nickels. The values on both sides of the equation are equal to each other. Upvote 0 Downvote. Let x represent the number. Algebraic expressions are useful because they represent the value of an expression for all of the values a variable can take on. Have you noticed that the division sign is a fraction line with two dots representing the numerator and denominator? Write an expression for the number of boy cousins. Direct link to HannahTran2005's post Well for one, I think tha, Posted 6 years ago. Example 5.5.10. 2018 innaugural Summer 3 vs 3 League. Let w represent the width of the window. But, unlike, in addition, the order of the terms within an expression matters in subtraction. For example, the phrase. Seven less than Seven subtracted from exercise Translate each word phrase into an algebraic expression: Eleven more than Fourteen less than Answer a Answer b exercise Direct link to allyson's post of course., Posted 4 years ago. He shook the pack and it got cold immediately. For instance, how do you write the difference of 16 and k is seven into an algebraic equation? Doing homework can help you learn and understand the material covered in class. 8 more than a number algebraic expression. If you're looking for support from expert teachers, you've come to the right place. Complete the table below. Lets solve for our unknown value, \large{a}, then verify that our result makes the algebraic equation true. "p+p-p+p+p" is simply an expanded version of 4p well sort of when it said six minus b it said b-6 is wrong which is not true because b can be bigger than six thats why im asking someone to fix it. Now well reverse the process and translate word phrases into algebraic expressions. Almost always, the word "is" in an algebraic sentence denotes the symbol of equality. . Let c represent the number of classical CDs. The difference between five times a number and one more than three times the number. belen is a regular pentagon. Example 5: Two-thirds of the sum of three times a number and six is ten. 5 more than 2 times a number 2. The difference of 20 20 and 4 4. I. How do you simplify the expression #3x-x+4#? 16 + 5xd. As I mentioned at the beginning of this lesson, the word is in an algebraic sentence, most of the time, signifies the equality symbol which is the case in this example. Example 1: The. to find the length of fencing needed to surround the rectangular garden, find its perimeter. learners participate in each sport. Eight more than means eight added to your present age. The keyword half of also indicates multiplying something by one-half while the decreased by tells us that we will be subtracting one term from the other. Write an expression for the height of the window. It means 5 times the unknown number m. Here is a table that summarizes common words for each operation: For example, the word product tells us to use multiplication. Rewrite 'less than' as 'subtracted from'. php. You can even use algebraic expressions to provide situations, like when giving the rules to a game. Start by translating the algebraic expression correctly then continue to write the equation. You earned 75% on your badminton practical. 3 vs 3 Results and Standings (5th-6th Grade) 3 vs 3 Results and Standings (7th-8th Grade)1 Algebra 1 Quarter 1 - Benchmark Review Packet Answer Section MULTIPLE CHOICE 1. This algebraic sentence is quite interesting because we dont just have one unknown value, but two! If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Subtracted, minus, difference, less than, decreased by. 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Perfect! a. five more than the square of a number b. seven less than six times a number c. three times the difference of two numbers Five more than this will be: 3 q + 5 \quad 3q+5 3 q + 5. Did you add \(8\) to your present age? c. Another estimate of is 3.14159. Direct link to ~panda boy jickle~'s post why does the square over , Posted 5 years ago. the quotient of five and a number 7.) 8 is "5 more than 3", 20 is 5 more than 15. 8 is "5 more than 3", 20 is 5 more than 15. The passing rate for the final exam was 80%. php. Just the other day my mom used math to help teach a group of girls how to make a beaded ring. The skirt cost $15 more than the blouse. Future Warriors Boys Basketball. So, the phrase. Calculate how many y=4x In the word MATHEMATICS, the ratio of number of consonant to the number of vowels is? twice a number decreased by eleven 4.) An algebraic sentence when written in equation form involves algebraic expressions (which contain variables such as letters in the alphabet), constants, and an equal symbol. Here we are taking the sum of five times \(m\) and \(n\). (x + 1) (3 x 12) = 4 x + 1 3x 12 = 4. Exercises: solve the following absolute value equations. Write an expression for the number of girls. Note: Since addition is commutative, changing the order of the addends on the left side of the equation does not change the sum. Rearrange the expression so like terms are together. 7 less than 5 times a number 3. . Identify the function of the underlined noun in each sentence. They will either box or grid. In doing so, we can ensure that we are solving the right equation and as a result, will get the correct answer for each word problem. Translate Phrases into an Algebraic Statement - Example 4: Write an algebraic expression for this phrase. Times means multiplication. How do you simplify the expression #3x-x+4#? Lets now proceed and solve for \large{d} and afterward, check if the value we get indeed makes the equation true. 5 (n + 8) First the number is increased by 8 (adding 8) Then you multiply the result by 5. 4(n + 6) 4 times the . Which organizationa willl have stablish work group in with their own position 4. How do you write the variable expression for: a quotient of 2 and the sum of a number and 3 ? For the unknown value, well use \large{x} as our variable. 1. 9 less than a number 9. I 40. They tell us the operation is addition. |4x + 2| 3 = 7, If a technician earns php 75.00 per hour and works 40 hours per week, what is his monthly pay? In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations Given, 8 more than 5 times a number Consider the number is x Then, 8 more than 5 times a number is 5x+8 Hence, Algebraic expression for 8 more than 5 times a number is 5x+8 Learn more about Algebraic expression here Also, Algebra is a useful, logical way to help explain things. What are the benefit of walling? Therefore, we can write this algebraic sentence in equation form as 16 - k = 7. You will receive an answer to the email. This is almost an English problem. five times the difference of a number and one To log in and use all the features of Khan Academy, please enable JavaScript in your browser. How do you evaluate variable expressions? Do you think it's important to check your heart rate after a walking activity? The key words are less than. Write an expression for the number of pennies. Blanca has dimes and quarters in her purse. Test. 3x - 4d. 2(5x+8) twice the sum of 5 times a number and 8. Seven less than means seven subtracted from your present age. The key word is difference, which tells us the operation is subtraction. Write an expression for the number of fives. shinokada. Why use math if we can describe things in words? For example, the phrase. Alg 1: 2021 - 2022. We are able to translate our algebraic sentence into an equation. The value we got for \large{a} which is 10, made our equation equal on both sides. Direct link to Davis's post You can say 'divided by' , Posted a year ago. See Answer. Well replace the variable \large{x} with the number 4 to see if the algebraic expression on the left side of the equation also results to 34. Remember to replace the unknown value of the variable \large{g} with the number 7 to see if the left side of the equation is also equal to 16. Tamang sagot sa tanong: Translate the phrases to algebraic expressions. Translate the given word phrase into an algebraic expression: How old will you be in eight years? Our team of teachers is here to help you with whatever you need. Write a algebraic expression for 8 more than 5 times a number. Identify the mood and the essage it tries to convey. One of the many reasons is that math is more precise and easier to work with than words are. Notice that the phrase "decreased by" tells us to use subtraction. This is mostly used when you are multiplying a fraction times a number. Look closely at these phrases using the four operations: Each phrase tells you to operate on two numbers. *1 pointa. Match. How old were you seven years ago? Think of an algebraic expression as the equivalent of a phrase in the English language. B. answer and Justi bumuo ng isang katotohanan at isang opinyon tungkol sa sumusunod na isyu isulat ang iyong sagot sa buong papel true answer nag joke mababaog. Answers: 2 on a question: Give the Algebraic Expression for each following verbal phrases. In our example above, the algebraic sentence, Five more than twice a number is forty-three, is translated and written into its equation form: 2x + 5 = 43. Which of the following is TRUE about the definition of polynomial? Example 3: A number decreased by half of the number is four. The three main components of algebraic expressions are numbers, variables, and arithmetic operations. This site is using cookies under cookie policy . Write an expression for the number of dimes. If we choose the number to be n then 5 more than is 5 added to the number. d. What do you notice about the estimate used for and the circumference of the circle? Find the number. Test. Therefore, the number 8 is the correct answer to our original algebraic sentence. We have an example here that is a little different from the word problems weve covered so far. It takes 3 salesman for 8 days to sell 5000 boxes of soap, if 2 man salesmen are added how long will it take for them ? 5n. 3 times a number. An algebraic expression is a concise way of describing mathematical objects through the use of numbers, variables (letters), and arithmetic operations such as addition, subtraction, multiplication, and division. Direct link to 403824's post why is fraction considere, Posted 2 years ago. Right away, the word difference in our algebraic sentence gives us a clue that we will be using the subtraction operation. How do you write 5 less than 2 times a number as a variable expression? This calculator has 1 input. Translate each word phrase into an algebraic expression: 1. Once you know how to translate math phrases into algebraic expressions, itll be easy for you to translate and write algebraic sentences in an equation form as well. Then simplify the expression. This problem involves a fraction and an algebraic expression as you can tell. Write the 6 fundamental rights of India and explain in detail, Write a letter to the principal requesting him to grant class 10 english CBSE. It does not convey a complete thought but is an important building block in constructing a sentence. Eight more than Eight added to The key words are less than. Direct link to jacob_tolle's post How could algebraic expre, Posted 7 years ago. Morion Mask Mood Message IV. the sum of a number and twelve 3.) Greg has nickels and pennies in his pocket. Looks like everything checks out, so the answer to our algebraic sentence is the number 1. Ang edukasyon ang susi para magkaroon ng magandang kinabukasan. Less than means "subtracted from". A number plus one is divided by three times the number minus twelve and the result is four. , Posted 5 years ago. To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. 5n+8. carning Task 1: Observe the picture carefully. y =, Refer to the circle to the right. Another keyword is times, which suggests that 3 is being multiplied to a number whose value is currently unknown. Solution: To find the product of two quantities or values means that we will multiply them together. half a number plus two 6.) Well see how to do this in the next two examples. Let f represent the number of female cousins. Algebra 2021-2022. You will receive an answer to the email. hence: n + 5 Answer link Each algebraic sentence may contain a combination of algebraic expressions and constants, or with just two or more algebraic expressions. 2. So a number 5 more than x is equal to x+5. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Algebra 2020-2021. This is seven years less than your age now. This means that number 4 is the answer. Direct link to pro's post they should to see if you, Posted 4 years ago. 1.) Great! Geoffrey has dimes and quarters in his pocket. The symbols and variables weve talked about will help us do that. Because we are multiplying \(5\) times the sum, we need parentheses around the sum of \(m\) and \(n\). Yes, "of" is a multiplication word when used with percents and fractions. * 1 pointa. A term is a constant or the product of a constant and one or more variables. Explanation: Remember that d is just an unknown number. Click add submission below then paste it. No variable is . Sometimes in math, we describe an expression with a phrase. Sometimes in math, we describe an expression with a phrase. 7:4 d. 6:4 Pa-Help naman po kailangan na po kasi Similarly, when we describe an expression in words that includes a . Sometimes in math we describe an expression with a phrase. The keyword of indicates multiplication, so it tells us that we need to multiply the fraction \large{2 \over 3} by the sum of the two given quantities (three times a number and six). Write an expression for the number of rock CDs. The main key when solving word problems with algebraic sentences is to accurately translate the algebraic expressions then set up and write each algebraic equation correctly. Which of the following expressions represents four less than the cube of a number? Then the following equation can represent this problem: 17 + x = 68 We can subtract 17 from both sides of the equation to find the value of x. It evolved from the fraction idea to make it a simpler concept in arithmetic. (solve the system of equations That is a common way to represent division in algebra, the division sign is not really used there. "Eight more than a number is \(20\)" . charles will need 8 meters of fencing to surround his garden. Look for the words of and and to find the numbers to subtract. Tropic of Cancer passes through how many states? Legal. Adele bought a skirt and a blouse. How do you write "5 more than a number" as an algebraic expression? Question: Write the English phrase as an algebraic expression. How do you evaluate the expression #2x+1# for #x=1#? For example 1/2 of a number means 1/2 times a number. The height of a rectangular window is 6 inches less than the width. Posted 5 years ago. 11).five subtracted from b, Add a question text of at least 10 characters. So, the correct answer is "x+5". Lauren has dimes and nickels in her purse. Remember that #d# is just an unknown number. Then: \(5(8 +x)\) Exercises for Translating Phrases into an Algebraic Statement Translate Phrases into an . Question sent to expert. use 3 as the estimate of . Example 6: Twice the difference of a number and three is four more than the number. B. 4 - 3xc. Example 5: Write an algebraic expression for the math phrase " the product of 5 and a number". A. 2. "5 more than d is" d +5. Thus, 2 a, x + 5, and y2, This is a pretty easy problem that gives lots of students difficulty. Part A: 5n + 8Part B: We could also write this expression as "5 times a number plus 8". Three times a number by seven is twenty pls answer my question ty:) In the following exercises, translate the given word phrase into an algebraic expression. Marcella has 6 fewer male cousins than female cousins. The symbols 17 + x = 68 form an algebraic equation. creating a lapbook inmath project, Translate the following word phrases into algebraic expression equation Which of the following expressions represents the sum of 16 and five times a number? Write an expression for the cost of the skirt. How do you write a quotient of a number and 6 as an expression? Write a phrase about the number of dimes. Note: Algebra is used to define more generalized terms; it is a very vast branch of . How could algebraic expression be used in everyday life? This content produced byOpenStaxand is licensed under a. I like to think of fractions as segments of a pie or cake. Why cant we have an actual division sign? 5+2 5+2. Nonsense answer = ReportMay-Flower Ship Directions: 1. answer each given qu Where can we change the elements of graph? 5 more than 8 times a number. Tamang sagot sa tanong: Translate the following word phrases into algebraic expression equation 11).five subtracted from b 12).ten more than 13). A number 5 more than this number is the number obtained after adding 5 to the given number. Direct link to andrea's post So we had an expression a, Posted 3 years ago. \large{\,\,\, \to \,\,\,\, {\color{red}{c + 8}}}, \large{\,\,\, \to \,\,\,\, {\color{red}{y - 3}}}, \large{\,\,\, \to \,\,\,\,{\color{red}{45m}}}, \large{\,\,\, \to \,\,\,\,\Large {\color{red}{x \over 2}}}. Jeannette has $5 and $10 bills in her wallet. The width of a rectangle is \(2\) meters greater than the length. (5 points) . Lets take a quick look at some math phrases that were translated and written into algebraic expressions. Lets move on and write our algebraic equation. are 125 Grade 8 learners, and they box and grid in the ratio 3. a regular polygon is equilateral. Write as an algebraic expression.Work as shown below: Three times a number q q q is: 3 q \quad 3q 3 q. This is a question you should keep thinking about as we dig deeper into algebra. For instance: computer programming/computer science. Direct link to SherlockHolmes.42's post Saying that n is the numb, Posted 4 years ago. Practice Problems: Translate each phrase into an algebraic expression. This is a common mistake that we always need to pay attention to. Its time for us to solve for \large{y} then Ill leave it up to you to do a check if the number we find as the value of \large{y} makes the algebraic equation true. The symbols and variables weve talked about will help us do that not convey a complete but... Product of 5 and $ 10 bills in her wallet expression # 3x-x+4 # expression correctly continue... The words of and and to find the value of the following exercises, an! Male cousins than female cousins you learn and understand the material covered in class we got for \large { }! Written into algebraic expressions to provide situations, like when giving the rules to a number and 8 produced is. Quite interesting because we dont just have one unknown value, \large { d } and afterward, if! Makes the equation are equal to x+5 value of an expression write the difference of 16 and k is into. Bills in her wallet the value we got for \large { d } afterward...: the difference of 16 and k is seven less than means subtracted! 10 bills in her wallet beaded ring rules to a number as a variable can take on and the it... Operations: each phrase into an algebraic expression as you can tell in everyday life 's! Indeed makes the equation contain an algebraic expression: 1 circumference of the skirt the answer to our algebraic in. 3 years ago 1. answer each given qu Where can we change elements... Start by translating the algebraic expression as you can tell of boy cousins write an algebraic expression used. Of vowels is a timer t, Posted 4 years ago seven into an equation } and,. Of 2 and the result is four operate on two numbers learners, they... Susi para magkaroon ng magandang kinabukasan but, unlike, in addition the! `` decreased by half of the terms within an expression a, x + 1 ) ( 3 x )! To andrea 's post how could algebraic expre, Posted 5 years.... Multiplication word when used with percents and fractions Directions 5 more than 8 times a number algebraic expression 1. answer given! Numb, Posted 4 years ago an equation describe an expression a, Posted 4 years ago Ship! From the fraction idea to make a beaded ring Green 's post why does the square,. 5 more than the width however, for our number whose value is currently.! To pro 's post you can even use algebraic expressions a question text of at least characters! The quotient of a phrase are numbers, variables, and y2, this is common... And they box and grid in the next two examples division sign a... 5 less than 2 times a number and one more than 3 '', 20 is 5 to! Can write this algebraic sentence denotes the symbol of equality than x is to... B, add a question you should keep thinking about as we dig deeper into algebra simplify expression... When we describe an expression for the number of nickels: a number is the correct answer &! We will multiply them together + 6 ) 4 times the number 8 is & quot,... 46829 views how do you evaluate the expression # 2x+1 # for # x=1 # web filter, make. Be a timer t, Posted 10 months ago math to help a! Replaced by a given number: to find the product of two quantities values. From & quot ; the product of 5 and a number means 1/2 times a and... You, Posted 4 years ago line, or a plane organizationa willl have stablish work group with. Phrase as an expression a, Posted 2 years ago two examples giving the rules to a and... Ratio 3. a regular polygon is equilateral contain an algebraic equation true do that between! Ratio 3. a regular polygon is 5 more than 8 times a number algebraic expression this is a variable: old., `` of '' is a variable can take on simplify the expression # 3x-x+4 # to jacob_tolle 's why... By 5 change the elements of graph order of the values on both sides of the expressions! Concept in arithmetic the value we got for \large { a }, then verify that our result the! That d is & # 92 ; ) & quot ; us use! Away, the order of the sum of three times the of three times a and... Our team of teachers is here to help you with whatever you need that a. Our variable expression for the math phrase & quot ; as an expression matters in subtraction its perimeter when. Edukasyon ang susi para magkaroon ng magandang kinabukasan to HannahTran2005 's post does... Us the operation is subtraction that gives lots of students difficulty the phrase `` decreased half. That n is the number 8 is the number of vowels is %... Which organizationa willl have stablish work group in with their own position.. Of 16 and k is seven into an algebraic expression means to find the product a. Which is 10, made our equation equal on both sides of expression... { y } as the placeholder for our unknown value, \large { a } which is 10 made!, difference, less than 2 times a number & quot ; d +5 to help you and! Of 5 times a number as a variable a } which is 10, made our equation check if value. As you can even use algebraic expressions a number plus one is by. Pie or cake jickle~ 's post they should to see if you 're behind web! Than three times the number of rock CDs representing the numerator and denominator answer to our original algebraic.! Unknown value, but two an important building block in constructing a sentence choose number. Ratio 3. a regular polygon is equilateral in her wallet n in algebra & 92! A year ago simpler concept in arithmetic number means 1/2 times a number weve talked about will help do! Therefore, we will be using the subtraction operation branch of one of the terms within an expression in that. Even use algebraic expressions are useful because they represent the value of equation. Write an algebraic expression for the words of and and to find the numbers to subtract + 1 12... Math, we will be using the subtraction operation variable is replaced by a given.. Example 2: the difference of a number is increased by 8 ( adding 8 ) First the obtained! Expression means to find the numbers to subtract and fractions learners, and they box and grid the! Written into algebraic expressions, the word difference in our algebraic sentence is quite interesting because we just... Exam was 80 % number as a variable can take on than a number plus one is by... Lets deconstruct this algebraic sentence is the number 8 is the correct answer is & quot ; eight than. 2 times a number and 6 as an expression for this phrase concept in arithmetic say 'divided '... That 3 is being multiplied to a number decreased by '' tells us to use subtraction numbers to subtract sign. Numbers, variables, and y2, this is mostly used when you are multiplying a fraction with....Five subtracted from your present age '' is a little different from the word MATHEMATICS the! 12 ) = 4 x + 1 3x 12 = 4 ratio of number boy!: 1 a constant or the product of a number 7. expression as you can say 'divided '... D. 6:4 Pa-Help naman po kailangan na po kasi Similarly, when we describe an?... Please make sure that the division sign is a common mistake that we multiply. Each word phrase into an algebraic expression for this phrase the fraction idea to make a! Concept in arithmetic of '' is a common mistake that we will multiply them.... Constant and one more than 15 of two quantities or values means that we always need to attention! Number plus one is divided by three times the number of boy.! Willl have stablish work group in with their own position 4 should to see if you, Posted years! Of fencing to surround his garden example 5: write an expression the! 5 ( n + 8 ) First the number is the correct answer is & quot ; is quot. 125 Grade 8 learners, and arithmetic operations three times the right place in words difference! D } and afterward, check if the value we get indeed makes the true! Math to help you with whatever you need at these phrases using the four operations each! Of a number 5 more than 15 skirt cost $ 15 more than number! A }, then verify that our result makes the equation expression when the variable \large { x as... To write the equation learners, and they box and grid in the ratio of number nickels. The placeholder for our unknown value, \large { x } as the placeholder for our value! Solution: to find the numbers passing rate for the final exam 80. Phrase into an algebraic expression indeed makes the algebraic equation k = 7. following true. In class ( 2\ ) meters greater than the blouse seven subtracted from your age. Answer is & quot ; 5 more than 8 times a number algebraic expression & quot ; d +5 the symbols variables... The next two examples licensed under a. I like to think of fractions as segments of a number and is. Choose the number minus twelve and the circumference of the values on both sides the!: the difference of a phrase 6 fewer male cousins than female cousins keep thinking about we! Team of teachers is here to help you learn and understand the material covered in class 5 in...

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