Decimals with Fractions - PSAT Math

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Question

Write 0.45 as a fraction.

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Answer

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Question

Express as a fraction: $0.3$\overline{4}$$

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Answer

Let $x = 0.3$\overline{4}$ = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = $\frac{31}{90}$$

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Question

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

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Answer

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

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Question

Which of the following numbers is between 1/5 and 1/6?

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Answer

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

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Question

Write 0.45 as a fraction.

Tap to reveal answer

Answer

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Question

Express as a fraction: $0.3$\overline{4}$$

Tap to reveal answer

Answer

Let $x = 0.3$\overline{4}$ = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = $\frac{31}{90}$$

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Question

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

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Answer

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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Question

$$\frac{1}{10}$\times $\frac{3}{5}$\div $\frac{6}{7}$= {?}}$

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Answer

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Question

How much less is $\frac{1}{16}$ than ?

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Answer

$\frac{1}{16}$=.0625

.0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

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Question

Express as a decimal: $\frac{16}{9}$

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Answer

Divide 16 by 9:

The "7" repeats forever, so

$\frac{16}{9}$ = 1.$\overline{7}$

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Question

Express as a decimal: $\frac{9}{16}$

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Answer

Divide 9 by 16:

$$\frac{9}{16}$ = 0.5625$

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Question

Convert the fraction to a decimal.

$\frac{13}{25}$

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Answer

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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Question

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

Tap to reveal answer

Answer

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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Question

$$\frac{1}{10}$\times $\frac{3}{5}$\div $\frac{6}{7}$= {?}}$

Tap to reveal answer

Answer

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Question

How much less is $\frac{1}{16}$ than ?

Tap to reveal answer

Answer

$\frac{1}{16}$=.0625

.0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

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Question

Express as a decimal: $\frac{16}{9}$

Tap to reveal answer

Answer

Divide 16 by 9:

The "7" repeats forever, so

$\frac{16}{9}$ = 1.$\overline{7}$

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Question

Express as a decimal: $\frac{9}{16}$

Tap to reveal answer

Answer

Divide 9 by 16:

$$\frac{9}{16}$ = 0.5625$

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Question

Convert the fraction to a decimal.

$\frac{13}{25}$

Tap to reveal answer

Answer

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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Question

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

Tap to reveal answer

Answer

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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Question

$$\frac{1}{10}$\times $\frac{3}{5}$\div $\frac{6}{7}$= {?}}$

Tap to reveal answer

Answer

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Decimals with Fractions - PSAT Math

Write 0.45 as a fraction.

.45 is equivalent to 45 out of 100, or . Divide both the numerator and denominator by 5 to simplify the fraction:

Express as a fraction:

Let Then and Subtract:

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

Which of the following numbers is between 1/5 and 1/6?

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

Write 0.45 as a fraction.

.45 is equivalent to 45 out of 100, or . Divide both the numerator and denominator by 5 to simplify the fraction:

Express as a fraction:

Let Then and Subtract:

The ogre under the bridge eats of a pizza and then throws the rest of the pizza to the rats. The rats eat of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left. 1/4 * 1/5 = 1/20 = 5%

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

How much less is than ?

$\frac{1}{16}$=.0625 .0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

Express as a decimal:

Divide 16 by 9: The "7" repeats forever, so

Express as a decimal:

Divide 9 by 16:

Convert the fraction to a decimal.

We can multiply our numerator and denominator by , which leads to . From here we divide by our denominator, moving the decimal two places to the left.

The ogre under the bridge eats of a pizza and then throws the rest of the pizza to the rats. The rats eat of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left. 1/4 * 1/5 = 1/20 = 5%

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

How much less is than ?

$\frac{1}{16}$=.0625 .0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

Express as a decimal:

Divide 16 by 9: The "7" repeats forever, so

Express as a decimal:

Divide 9 by 16:

Convert the fraction to a decimal.

We can multiply our numerator and denominator by , which leads to . From here we divide by our denominator, moving the decimal two places to the left.

The ogre under the bridge eats of a pizza and then throws the rest of the pizza to the rats. The rats eat of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left. 1/4 * 1/5 = 1/20 = 5%

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

Express as a fraction: $0.3$\overline{4}$$

Let $x = 0.3$\overline{4}$ = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = $\frac{31}{90}$$

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

Express as a fraction: $0.3$\overline{4}$$

Let $x = 0.3$\overline{4}$ = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

$\underline{10 x = ; ; 3.444...}$

$x = $\frac{31}{90}$$

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

How much less is $\frac{1}{16}$ than ?

$\frac{1}{16}$=.0625

.0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

Express as a decimal: $\frac{16}{9}$

Divide 16 by 9:

The "7" repeats forever, so

$\frac{16}{9}$ = 1.$\overline{7}$

Express as a decimal: $\frac{9}{16}$

Divide 9 by 16:

$$\frac{9}{16}$ = 0.5625$

Convert the fraction to a decimal.

$\frac{13}{25}$

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

How much less is $\frac{1}{16}$ than ?

$\frac{1}{16}$=.0625

.0665-.0625=.004=\frac{4}{1000}$=\frac{1}{250}$

Express as a decimal: $\frac{16}{9}$

Divide 16 by 9:

The "7" repeats forever, so

$\frac{16}{9}$ = 1.$\overline{7}$

Express as a decimal: $\frac{9}{16}$

Divide 9 by 16:

$$\frac{9}{16}$ = 0.5625$

Convert the fraction to a decimal.

$\frac{13}{25}$

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

The ogre under the bridge eats $\frac{4}{5}$ of a pizza and then throws the rest of the pizza to the rats. The rats eat $\frac{3}{4}$ of what is left. What fraction of the pizza is left when the rats are done?

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%