How to multiply fractions - SSAT Middle Level Quantitative

Card 0 of 1216

Question

Fill in the blank with the correct sign.

$\small 8$ __________ $\small 8\times\frac{1}{5}$

Answer

$\small 8$ __________ $\small 8\times\frac{1}{5}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{8}{1}\times\frac{1}{5}=\frac{8}{5}$

$\small \frac{8}{5}=1\frac{3}{5}$ Because $\small 5$ can go into $\small 8$ only $\small 1$ time and $\small \frac{3}{5}$ is left over.

$\small 8>1\frac{3}{5}$

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Question

Fill in the blank with the correct sign.

$\small 2\times\frac{1}{2}$ __________

Answer

$\small 2\times\frac{1}{2}$ __________

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

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

$\small \frac{2}{2}=1$ Because can go into an even $\small 1$ time.

$\small 1<2$

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Question

Fill in the blank with the correct sign.

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

Answer

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{9}{1}\times\frac{2}{3}=\frac{18}{3}$

$\small \frac{18}{3}=6$ Because can go into $\small 18$ and even times.

$\small 9>6$

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Question

Evaluate:

Answer

By order of operations, perform the rightmost addition (the one within the parentheses) first, the multiplication second. and the leftmost addition last.

$1.2 + 0.6 (0.5 + 2.3) = 1.2 + 0.6 \cdot 2.8 = 1.2 + 1.68 = 2.88$

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Question

Express the product in simplest form:

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5}$

Answer

Rewrite the mixed fractions as improper fractions, cross-cancel, and multiply across:

$\frac{5}{7} \cdot 1 \frac{1}{7} \cdot 2 \frac{4}{5} = \frac{5}{7} \cdot \frac{8}{7} \cdot \frac{14}{5}= \frac{1}{1} \cdot \frac{8}{7} \cdot \frac{2}{1}= \frac{16}{7}= 2\frac{2}{7}$

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Question

Evaluate:

$6.5 + 1.4 \times 1.6$

Answer

By order of operations, multiply first:

$1.4 \times 1.6$

Multiply 14 by 16, and position the decimal point so that two digits are right of it:

$14 \times 16 = 224$

$1.4 \times 1.6 = 2.24$

Now add this product to 6.5:

$6.5 + 1.4 \times 1.6 = 6.5 + 2.24$

Append a zero to the 6.5, and align the decimal points:

$\underline{2.24}$

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Question

Evaluate:

$5.96 + 3.2 \times 1.5$

Answer

By order of operations, multiply first:

$3.2 \times 1.5$

Multiply 32 by 15, and position the decimal point so that two digits are right of it:

$32 \times 15 = 480$

$3.2 \times 1.5 = 4.80 = 4.8$

Now add this product to 5.96:

$5.96 + 3.2 \times 1.5 = 5.96 + 4.8$

Append a zero to the 4.8, and align the decimal points:

$\underline{4.80}$

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Question

Evaluate:

$20.1 \cdot (-20.3)$

Answer

The product of two numbers of unlike sign is the (negative) opposite of the product of their absolute values.

$20.1 \cdot (-20.3) = - \left (20.1 \cdot 20.3 \right )$

There are a total of two digits to the right of the two decimal points. Therefore, the product can be calculated by multiplying 201 by 203, then placing the decimal point so that there are three digits at right.

$201 \cdot 203 = 40,803 \Rightarrow 20.1 \cdot 20.3 = 408.03$

Since we need to affix a negative symbol in front, the answer is

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Question

$\frac{3}{5} \times \frac{1}{6} =$

Answer

When multiplying a fraction, simply multiply straight across - numerator times numerator, denominator times denominator. When you do that, you should get this answer:

$\tfrac{3}{5} \times \tfrac{1}{6} = \tfrac{3}{30}$

Do not forget to reduce. 3 and 30 can both be evenly divided by 3, which would give you $\tfrac{1}{10}$ as your answer.

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Question

One euro is worth approximately $1.27. For how much American money can a French tourist expect to exchange 800 euros?

Answer

One Euro is equivalent to $1.27, so multiply the number of euros - 800 - by this conversion factor.

$$1.27 \times 800 = $ 1,016$

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Question

Multiply:

$0.58 \times 8.3$

Answer

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

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Question

Multiply: $6.73 \times 0.006$

Answer

First, remove the decimal points, multiplying as follows:

$673 \times 6 = 4 038$

Between them, the two factors have five digits to the right of their decimal points, so position the decimal point in the product so that there are five digits to the right. This will require placing a zero in front as a placeholder, so the final result is

$6.73 \times 0.006 = 0.04038$

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Question

$\frac{1}{3} \times \frac{4}{5}=?$

Answer

Multiply the numerators together, and then multiply the denominators together:

$\frac{1}{3} \times \frac{4}{5}=\frac{1\times 4}{3\times 5}=\frac{4}{15}$

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Question

Find $\frac{3}{5}\cdot \frac{7}{9}$ .

Answer

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{3}{5}\cdot \frac{7}{9}=\frac{21}{45}$ , which can be reduced to $\frac{7}{15}$ .

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Question

Find $\frac{5}{7}\cdot \frac{3}{4}=$ .

Answer

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{5}{7}\cdot \frac{3}{4}=\frac{15}{28}$

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Question

What is the product of the two fractions below?

$\frac{4}{5}\cdot\frac{7}{8}$

Answer

To solve for this expression, first multiple the numerators, and then multiply the demonators.

$\frac{4}{5}\cdot\frac{7}{8}$

$\frac{4\times7}{5\times8}$

$\frac{28}{40}$

Simplify the fraction by removing a common factor.

$\frac{28\div4}{40\div4}=\frac{7}{10}$

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Question

Which of the following statements demonstrates the identity property of multiplication?

Answer

The identity property of multiplication states that there is a number 1, called the multiplicative identity, that can be multiplied by any number to obtain that number. Of the four statements,

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

demonstrates this property.

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Question

Evaluate:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

Answer

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and a subtraction present, carry them out in that order. Finally, carry out the remaining subtraction:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

$= 15 - \left ( 2- \frac{4}{3}\right )$

$= 15 - \frac{2}{3}$

$= 14 \frac{1}{3}$

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Question

Raise to the fourth power.

Answer

To raise a negative number to an even-numbered power, raise its absolute value to that power:

$(-8)^{4}= 8^{4} = 8 \times 8 \times 8 \times 8 = 4,096$

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Question

Evaluate:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

Answer

By the order of operations, carry out the operation in parentheses, which is the rightmost subtraction, then the multiplication, then the leftmost subtraction:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

$= 20 - 7.5 \times 1.8$

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