Equivalent fractions and comparing fractions | Khan Academy (2024)

FAQs

What are equivalent fractions answers? ›

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole.

We are using the benchmark fraction ½, and we know that half of 10 is 5. If we compare the fraction 9/10 with the benchmark ½ (or 5/10) we can tell that 9/10 is larger than the benchmark because 9 is larger than 5. The fraction 9/10 will go to the right of the benchmark on the number line.

We can show a fraction using a diagram. Using a circle, we show the denominator as the total number of slices the circle is divided into, and the numerator as the number of shaded or unshaded slices. We can also group the number of parts in a diagram to show different fractions.

It should be noted that if the denominators are different and the numerators are the same, then we can easily compare fractions by looking at their denominators. The fraction with a smaller denominator has a greater value and the fraction with a larger denominator has a smaller value. For example, 2/3 > 2/6.

To find equivalent fractions, we multiply the numerator and the denominator by the same number, so we need to multiply the denominator of 7 by a number that will give us 21. Since 3 multiplied by 7 gives us 21, we can find an equivalent fraction by multiplying both the numerator and denominator by 3.

They are fractions that may look different but actually represent the same quantity. 2/3 and 6/9 are examples of equivalent fractions. How do you explain equivalent fractions? They can be explained as fractions that have different numerators and denominators but represent the same value.

Students will first learn about comparing fractions as part of numbers and operations in fractions in 4th grade.

Equivalent Denominators

This is the easiest situation in which to compare fractions. If two fractions have equivalent denominators, then compare the numerators to determine which faction is greater. Students at the earliest stages of learning about fractions should be able to do this.

There are 7 kinds of fractions; Proper Fractions, Improper Fractions, Mixed Fractions, Like Fractions, Unit Fractions, Equivalent Fractions and Same Numerator Fractions.

An easy way to solve this is to divide 27 by 2 and look at the remainder. So, 27 / 2 = 13 with 1 leftover. We can express this remainder as a decimal or fraction representing a half (0.5 or 1/2). So we can see that half of 27 is 13.5 or 13 1/2.

What is the easiest way to compare fractions? ›

Compare the numerators of the fractions.

The one with the larger numerator is the greater fraction. So, the fraction 65/91 is greater than 63/91 because 65 is greater than 63. This means that the original fraction, 5/7, is greater than 9/13.

The trick is to find the “missing pieces” (or parts), of each fraction that make one whole, and compare these pieces — the fraction with the smallest missing piece is bigger (i.e., closer to one whole), or conversely, the fraction with the larger missing piece is smaller (i.e., closer to zero).

As long as the denominators are the same, the fraction with the greater numerator is the greater fraction, as it contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction, as it contains fewer parts of the whole.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators. For example the fraction 1/2 is equivalent to (or the same as) 25/50 or 500/1000. Each time the fraction in its simplest form is 'one half'.