Q&A for How to Understand Fractions

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What fraction is greater than 1?

Donagan

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Any fraction is greater than 1 if its numerator is greater than its denominator.

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Question

How many tenths are there in two and half?

Donagan

Top Answerer

There are 10 tenths in 1, 20 tenths in 2, and 5 tenths in one-half. So 2½ has 20 + 5 = 25 tenths.

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Question

I still don't understand how to simplify. How do I know what numbers to divide or multiply it by to equal the fraction/number you want it to be?

Donagan

Top Answerer

Simplifying a fraction means converting both the numerator and the denominator to smaller numbers while leaving the value of the fraction unchanged. The way to do this is to divide both numerator and denominator by the same small number (such as 2, 3, or 5) and perhaps doing it again and again until you can't reduce any further (remembering that you always want both the numerator and denominator to be whole numbers).

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How do I divide fractions?

Community Answer

Dividing by a fraction involves inverting the fraction and multiplying it by the other number. For example, to divide 8 by 4/5, first invert 4/5 to become 5/4. Then multiply 5/4 by 8, which equals 40/4, or 10. That's the answer. If "the other number" is also a fraction go through the same process. For example, to divide 7/10 by 2/3, invert 2/3 to become 3/2. Then multiply 3/2 by 7/10, which is 21/20, the answer.

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If 7/8 of a number is 42, what is the number?

Donagan

Top Answerer

Find the number by dividing 42 by 7/8. That's the same as multiplying 42 by 8/7, which equals 346/7 or 48. 48 is the number you're looking for. Verify by finding 7/8 of 48 (meaning multiplying 48 by 7/8, which is 336/8 or 42.).

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5/3 hour is how much time?

Donagan

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5/3 of an hour is one hour and 40 minutes.

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Question

Which fraction is greatest in the following: 2/15, 3/10, 4/21, 5/18?

Donagan

Top Answerer

We can simplify this a bit by comparing the first two fractions: 3/10 is greater than 2/15, because 3 is greater than 2, and 10 is less than 15. Also, 5/18 is greater than 4/21, because 5 is greater than 4, and 18 is less than 21. Therefore, neither 2/15 nor 4/21 can be the greatest fraction. Comparing 3/10 and 5/18, which one is greater isn't so obvious, so we convert both to fractions with a denominator of 10 x 18 = 180: 3/10 = 54/180, and 5/18 = 50/180, so 3/10 is the greatest of the four original fractions.

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Why after you multiplied the two denominators did you come up with 54 for 3/10?

Community Answer

The article example is considering a common denominator of 180 to compare 3/10 to another fraction. Multiplying both numerator and denominator of a fraction by 18 doesn't change its value, so 3/10 = (3*18)/(10*18) = 54/180.

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Of 73 cars making up a freight train, 49 are boxcars. What fractions of the cars are not boxcars?

Donagan

Top Answerer

(73 - 49) or 24 cars are not boxcars. So 24/73 of the cars are not boxcars.

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How do you work out which is the largest fraction out of 1/7, 5/7 and 4/7?

Community Answer

When the fractions you are comparing all have the same denominator (as in this case), just compare the numerators. Since 5 is the largest numerator, 5/7 is the largest of those fractions.

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Question

What steps do I follow when teaching 7/100 + 12/100 using a grid?

Community Answer

First mark off 100 units (vertically or horizontally) on the grid. Then color in seven consecutive units. That represents 7/100. Now color in the next twelve consecutive units (perhaps in a different color). That represents adding 12/100. The total length of the colored units is 19 units representing 19/100.

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Question

What is an equivalent fraction?

Community Answer

Equivalent fractions are different fractions that have the same value. An example: 1/2 = 2/4 = 3/6.

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