What Are Fractions?

A fraction is really a division statement. The number ½ says that we divided 1 whole thing into 2 equal parts. Similarly, ¾ indicates that we divided something -- say a pizza -- into 4 equal parts and we ate 3 of them. It could also mean that we have 4 things of equal size or value and 3 of them are of interest because of some quality, say they're red or they've been eaten. So if we ordered 4 pizzas and ate 3 of them, we'd have eaten ¾ of all the pizzas.

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Changing Fractions to Decimal Equivalents by Division

Here's some fraction images

Since a fraction indicates division, that's exactly how we change it into a decimal. We do the division. So, to get the decimal equivalent of ¾, we divide 4 into 3 like this:

However, if we're smart, we'll just remember that three "quarters" = 75 cents so ¾ = 0.75.

Repeating Decimals

When we use division to find the decimal equivalent of fractions with 3, 7, 9, 11 etc.in the denominator, the quotient is a repeating digit. These are called repeating decimals and as always in math, we use a precise symbol to denote them.

Let's use division to find the decimal equivalent of .

...

We must make sure the "bar" is over ALL THE REPEATING DIGITS in the pattern!

For instance,

and
Note that the bar covers all 6 repeating digits.

The decimal equivalent of 1/19 = 0.052631578947368421 052631578947368, with 18 repeating digits in the pattern. All 18 must be covered by the bar.

Changing the Denominator to a Power of 10

Since the denominator of any decimal's fraction equivalent is a power of 10, when we have to find a fraction equivalent to a decimal value, and it's easy to make the denominator a power of 10 through multiplication by a fraction equal to 1, we can proceed like this.

We know that 5 × 20 = 100 so we multiplied by 5/5 which equals 1 -- therefore we didn't change the value of our fraction -- we just wrote an equivalent fraction with a denominator of 100.
In the second case, we knew that 8 × 125 = 1000, so we multiplied by 8/8.

When we have mixed numbers -- part whole number, part fraction, we change the fraction part to its decimal equivalent and write the whole number as usual. So 1¼ = 1.25

Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

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Practice

1) Multiply by 1 to make the denominator a power of 10, then write the decimal equivalent.

a)

b)

c)

d)

e)

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2) Find the decimal equivalent by division. Round to 3 decimal places. Indicate repeats.

a)

b)

c)

d)

e)

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3) Write the fraction equivalent of these decimals. Reduce to lowest terms.

a) 0.36 =

b) 0.012 =

c) 0.6 =

d) 0.237 =

e) 0.0027 =

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Solutions

1) Change each denominator to a power of 10, then write the decimal equivalent.

a)	b)	c)
d)	e)

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2) Use division to find the decimal equivalent of these fractions. Round to 3 decimal places.

a) 0.267

b) 0.417

c) 0.714

d) 0.727

e) 0.444

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3) Write the fraction equivalent of these decimals. Reduce to lowest terms.

a) 0.36 =	b) 0.012 =	c) 0.6 =
d) 0.237 =	e) 0.0027 =

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Arithmetic MathRoom Index