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# Equivalent fractions and comparing fractions: FAQ

## What are equivalent fractions?

Equivalent fractions are fractions that look different but represent the same amount. For example, start fraction, 1, divided by, 2, end fraction, start fraction, 2, divided by, 4, end fraction, and start fraction, 3, divided by, 6, end fraction are all equivalent fractions.

## How can we find equivalent fractions?

We can use fraction models or number lines to find equivalent fractions.
For example, start color #543b78, start fraction, 6, divided by, 8, end fraction, end color #543b78 is at the same location on the number line as start color #0c7f99, start fraction, 3, divided by, 4, end fraction, end color #0c7f99.
Two rectangles sit on top of each other. The top rectangle shows one whole divided into four equal parts. Three parts are shaded. The rectangle on the bottom shows one whole divided into eight equal parts. Six parts are shaded. A number line below the rectangles shows tick marks above the number line from zero-fourths to four-fourths and tick marks below the number line from zero-eighths to eight-eighths. An orange point appears at the tick mark three-fourth, which is the same as six-eighths.
start color #0c7f99, 3, end color #0c7f99 pieces of start color #0c7f99, start fraction, 1, divided by, 4, end fraction, end color #0c7f99 has the same area as start color #543b78, 6, end color #543b78 pieces of start color #543b78, start fraction, 1, divided by, 8, end fraction, end color #543b78 .
Two circles equal in size. The top circle is divided into 4 equal parts. Three parts are shaded. The bottom circle is divided into 8 equal parts. Six parts are shaded. The same amount is shaded in both circles.

## How can we compare fractions with the same numerator?

When comparing fractions with the same numerator, the fraction with the smaller denominator will be larger. For example, if we compare start fraction, 1, divided by, 2, end fraction and start fraction, 1, divided by, 4, end fraction, we can see that start fraction, 1, divided by, 2, end fraction is larger because the denominator is smaller (so the single "part" is larger).

## How can we compare fractions with the same denominator?

When comparing fractions with the same denominator, the fraction with the larger numerator will be larger. For example, if we compare start fraction, 2, divided by, 4, end fraction and start fraction, 3, divided by, 4, end fraction, we can see that start fraction, 3, divided by, 4, end fraction is larger because the numerator is larger (so there are more "parts" in the fraction).

## Where do we use comparing fractions and equivalent fractions in the real world?

There are many potential real-world applications for comparing and working with equivalent fractions. For example, in cooking, we might need to use equivalent fractions in order to follow a recipe accurately if we don't have the right measuring cup on hand. We might also need to compare fractional measurements when sewing or doing carpentry work in order to cut a piece of material to the right size.