How to add fractions - ISEE Middle Level Quantitative Reasoning

Card 0 of 760

Question

Express the sum as a fraction in lowest terms:

$3 \frac{1}{2} + 5 \frac{1}{3} + 4 \frac{1}{4}$

Answer

Rewrite the fractions in terms of their least common denominator, 12.

Add, then rewrite as a mixed fraction:

$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{6}{12} + \frac{4}{12} + \frac{3}{12} =\frac{13}{12} = 1 \frac{1}{12}$

Add the integers:

Now add the sums:

$12 + 1 \frac{1}{12} = 13 \frac{1}{12}$

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Question

$\small \frac{3}{4}+\frac{1}{3}$

Answer

In order to add fractions we must find a common denominator. Since $\small 12$ is a multiple of both $\small 3$ and $\small 4$ , we must multiply the numerator and denominator of each fraction by a number to get a denomintor of $\small 12$ .

Since $\small 4$ times $\small 3$ is $\small 12$ , we can multiply the numerator and denominator of the first fraction by $\small 3$ .

$\small \frac{(3\cdot 3)}{(4\cdot 3)}= \frac{9}{12}$

Since $\small 3$ times $\small 4$ is $\small 12$ , we can multiply the numerator and demonimator of the second fraction by $\small 4$ .

$\small \frac{(1\cdot 4)}{(3\cdot 4)}=\frac{4}{12}$

Now we add together the numerators.

$\small \frac{9}{12}+\frac{4}{12}=\frac{13}{12}$

The answer is $\small \frac{13}{12}$ .

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Question

If a rectangle has a length of $\small \frac{1}{2}$ and a width of $\small \frac{1}{8}$ what is the perimeter of the rectangle, in simplest form?

Answer

In order to find the perimeter of a rectangle, you add together all the sides. In this particular case, however, you must first find a common denominator for all of the fractions. Luckily, $\small 8$ is a multiple of $\small 2$ , so we can multiply the numerator and denominator of $\small \frac{1}2{}$ by $\small 4$ to get a denominator of $\small 8$ .

$\small \frac{(1\cdot 4)}{(2\cdot 4)}=\frac{4}{8}$

Now we simply add all four sides.

$\small \frac{4}{8}+\frac{4}{8}+\frac{1}{8}+\frac{1}{8}=\frac{10}{8}$

Since $\small \frac{10}{8}$ can be reduced by dividing the numerator and denominator by $\small 2$ , we must simplify.

$\small \frac{(10/2)}{(8/2)}=\frac{5}{4}$

The perimeter of the rectangle is $\small \frac{5}{4}$ .

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Question

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

Which is the greater quantity?

(a)

(b)

Answer

Add both sides of the two equations:

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

$x + y = \frac{1}{2} + \frac{1}{3}+ \frac{1}{2} + \frac{2}{3}$

$x + y = \frac{1}{2} + \frac{1}{2}+ \frac{1}{3} + \frac{2}{3}$

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Question

$y -6 \frac{1}{10} = 7 \frac{2}{5}$

Which is the greater quantity?

(a)

(b)

Answer

(a)

(b) $y -6 \frac{1}{10} = 7 \frac{2}{5}$

$y -6 \frac{1}{10} + 6 \frac{1}{10} = 7 \frac{2}{5} + 6 \frac{1}{10}$

$y = 7 \frac{4}{10} + 6 \frac{1}{10} = 13 \frac {5}{10} = 13 \frac{1}{2}$

$13 \frac{1}{2} = 13.5 > 13.4$

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Question

Column A Column B

$\frac{2}{5}+\frac{1}{2}$ $\frac{1}{9}+\frac{7}{8}$

Answer

First, you must add the fractions in each column. When adding fractions, find the common denominator. The common denominator for Column A is 10. Then, change the numerators to reflect changing the denominators to give you $\frac{4}{10}+\frac{5}{10}$ . Combie the numerators to give you $\frac{9}{10}.$ Then, add the fractions in Column B. The common denominator for those fractions is 72. Therefore, you get $\frac{8}{72}+\frac{63}{72}$ . Combine the numerators to get $\frac{71}{72}$ . Compare those two fractions. Think of them as slices of pizza. There would be way more of Column B. Therefore, it is greater. Also, a little to trick to comparing fractions is cross-multiply. The side that has the biggest product is the greatest.

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Question

Which is the greater quantity?

(A) $\frac{3}{5} + \frac{1}{4}$

(B)

Answer

$\frac{3}{5} = 3 \div 5 = 0.6$ and $\frac{1}{4 } = 1 \div 4 = 0.25$ , so

$\frac{3}{5} + \frac{1}{4} = 0.6 + 0.25 = 0.85$ , the decimal equivalent of (A).

, the value of (B).

(A) is the greater.

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Question

$a=1.5,\ b = 4.5$

Which is the greater quantity?

(A) $b \div a$

(B)

Answer

$b \div a = 4.5 \div 1.5 = 3$

The two quantities are equal.

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Question

$\frac{2}{5} + \frac{1}{2} =$

Answer

When adding fractions with different denominators, you must first find a common denominator. Some multiples of 2 and 5 are:

2: 2, 4, 6, 8, 10...

5: 5, 10, 15, 20...

The first multiple 2 and 5 have in common is 10. Change each fraction accordingly so that the denominator of each is 10.

$\frac{2}{5} \times \frac{2}{2}\rightarrow\frac{4}{10}$

$\frac{1}{2}\times\frac{5}{5} \rightarrow \frac{5}{10}$

The problem now looks like this:

$\frac{4}{10} + \frac{5}{10} =$

Add the numerators once the denominators are equal. The result is your answer.

$\frac{4}{10} + \frac{5}{10} = \frac{4+5}{10}=\frac{9}{10}$

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Question

$\frac{1}{10} + \frac{2}{5} =$

Answer

When adding fractions with different denominators, first change the fractions so that the denominators are equal. To do this, find the least common multiple of 5 and 10. Some multiples of 5 and 10 are:

5: 5, 10, 15, 20...

10: 10, 20, 30, 40...

Since the first multiple shared by 5 and 10 is 10, change the fractions so that their denominators equal 10. $\tfrac{1}{10}$ already has a denominator of 10, so there is no need to change it.

$\frac{2}{5}\times\frac{2}{2}\rightarrow\frac{4}{10}$

The problem now looks like this:

$\frac{1}{10}+\frac{4}{10}=$

Add the fractions by finding the sum of the numerators.

$\frac{1}{10}+\frac{4}{10}=\frac{1+4}{10}=\frac{5}{10}$

When possible, always reduce your fraction. In this case, both 5 and 10 are divisible by 5.

$\frac{5}{10}\rightarrow\frac{1}{2}$

The result is your answer.

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Question

$\frac{2}{9} + \frac{1}{3} =$

Answer

When adding fractions with different denominators, first change the fractions so that the denominators are equal. To do this, find the least common multiple of 3 and 9. Some multiples of 3 and 9 are:

3: 3, 6, 9, 12...

9: 9, 18, 27, 36...

Since the first multiple shared by 3 and 9 is 9, change the fractions so that their denominators equal 9. $\tfrac{2}{9}$ already has a denominator of 9, so there is no need to change it.

$\frac{1}{3}\times\frac{3}{3}\rightarrow\frac{3}{9}$

The problem now looks like this:

$\frac{2}{9}+\frac{3}{9}=$

Solve by adding the numerators. The result is your answer.

$\frac{2}{9}+\frac{3}{9}=\frac{2+3}{9}=\frac{5}{9}$

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Question

Solve:

$\frac{3}{5}+\frac{1}3$

Answer

$\frac{3}{5}+\frac{1}3$

In order to solve this problem, we first have to find common denominators.

$\frac{3}5{} \times\frac{3}{3}=\frac{9}{15}$

$\frac{1}{3}\times\frac{5}{5}=\frac{5}{15}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{15}+\frac{5}{15}=\frac{14}{15}$

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Question

$\frac{1}{4}+\frac{1}{2}$

Answer

$\frac{1}{4}+\frac{1}{2}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{2}\times\frac{2}{2}=\frac{2}{4}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{1}{4}+\frac{2}{4}=\frac{3}{4}$

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Question

$\frac{1}{5}+\frac{1}{2}$

Answer

$\frac{1}{5}+\frac{1}{2}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{5}\times\frac{2}{2}=\frac{2}{10}$

$\frac{1}{2}\times \frac{5}{5}=\frac{5}{10}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{2}{10}+\frac{5}{10}=\frac{7}{10}$

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Question

$\frac{3}{4}+\frac{1}{3}=$

Answer

$\frac{3}{4}+\frac{1}{3}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$

$\frac{1}{3}\times\frac{4}{4}=\frac{4}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{12}+\frac{4}{12}=\frac{13}{12}$

$\frac{13}{12}=1\frac{1}{12}$ because can go into one time, with one left over.

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Question

$\frac{5}{6}+\frac{2}{4}$

Answer

$\frac{5}{6}+\frac{2}{4}$

In order to solve this problem, we first have to find common denominators.

$\frac{5}{6}\times\frac{2}{2}=\frac{10}{12}$

$\frac{2}{4}\times\frac{3}{3}=\frac{6}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{10}{12}+\frac{6}{12}=\frac{16}{12}$

$\frac{16}{12}=1\frac{4}{12}=1\frac{1}{3}$ because and go into one time with four left over. $\frac{4}{12}$ can be reduced to $\frac{1}{3}$ by dividing the numerator and the denominator by

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Question

Solve:

$\frac{2}{3}+\frac{1}2{}$

Answer

$\frac{2}{3}+\frac{1}2{}$

In order to solve this problem, we first have to find common denominators.

$\frac{2}{3}\times\frac{2}{2}=\frac{4}{6}$

$\frac{1}{2}\times\frac{}3{3}=\frac{3}{6}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{4}{6}+\frac{3}{6}=\frac{7}{6}$

$\frac{7}{6}=1\frac{1}{6}$ because can go into one time with $\frac{1}{6}$ left over.

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Question

Solve:

$\frac{1}{4}+\frac{4}{8}$

Answer

$\frac{1}{4}+\frac{4}{8}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{2}{8}+\frac{4}{8}=\frac{6}{8}$

$\frac{6}{8}\div\frac{2}{2}=\frac{3}{4}$

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Question

Solve the following:

$\frac{2}{3}+\frac{1}{7}$

Answer

$\frac{2}{3}+\frac{1}{7}$

In order to solve this problem, we first have to find common denominators.

$\frac{2}{3}\times\frac{7}{7}=\frac{14}{21}$

$\frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{14}{21}+\frac{3}{21}=\frac{17}{21}$

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Question

Solve:

$\frac{4}6{+\frac{3}{8}}$

Answer

$\frac{4}6{+\frac{3}{8}}$

In order to solve this problem, we first have to find common denominators.

$\frac{4}{6}\times\frac{4}{4}=\frac{16}{24}$

$\frac{3}{8}\times\frac{3}{3}=\frac{9}{24}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{16}{24}+\frac{9}{24}=\frac{25}{24}$

$\frac{25}{24}=1\frac{1}{24}$ because can go into one time with left over.

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