Understanding Equivalent Fractions

Revision of Fractions A fraction is a part of a whole. It is that simple! The top number is called the numerator. This tells you how many pieces of the whole you have. The bottom number is called the denominator. This tells you how many pieces make up the whole. The line in the middle of the fraction is called the fraction bar, or the vinculum. one piece out of three 1 3 numerator denominator

Unit Fractions A unit fraction is any fraction with a numerator of 1. Unit fractions represent one piece of a whole. One half, one third and one quarter are all examples of unit fractions. When ordering unit fractions from smallest to largest (or vice versa), there is one simple rule to help you. The larger the denominator, the smaller the unit fraction.

Ordering Unit Fractions Let’s use these circles to demonstrate this rule. 1 2 of a circle 1 3 of a circle 1 4 of a circle 1 8 of a circle 1 8 Which fraction is the smallest? The more pieces there are, the smaller the pieces become.

Ordering Unit Fractions As a class, order these fractions from smallest to largest. 1 3 of a bar 1 5 of a bar 1 2 of a bar 1 4 of a bar 1 5 , 1 4 , 1 3 , 1 2 smallest fraction largest fraction

Ordering Unit Fractions - Review Draw a number line into your workbook. Place these fractions on the number line in the correct position. 𝟏 𝟏𝟎 𝟏 𝟒 𝟏 𝟓 𝟏 𝟑 1 2 1

Equivalent Fractions Equivalent fractions are fractions which have the same value, even though they may be written differently. One half, two quarters and four eighths are equivalent fractions. They are different ways of expressing the same value. To find a fraction that is equivalent to another fraction, there is one simple rule to help you. Make equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number.

Making Equivalent Fractions Let’s use these squares to demonstrate this rule. 1 2 of a square 2 4 of a square 4 8 of a square = = x 2 x 2 1 2 = 2 4 = 4 8 x 2 x 2

Making Equivalent Fractions As a class, label these equivalent fractions. 2 6 of a bar 1 3 of a bar = ÷ 2 2 6 = 1 3 ÷ 2

Making Equivalent Fractions - Review Use multiplication or division to create three equivalent fractions for each of the fractions shown in the images below.

Lowest Terms We now know that fractions of the same value can be written in different ways e.g. 2 4 and 1 2 . Fractions should be written in the simplest possible way. To do this, you must reduce the fraction to its ‘lowest terms’ using the highest common factor of the numerator and denominator. To identify if a fraction is written in its lowest terms, there is one simple rule to help you. A fraction is written in its lowest terms when the numerator and the denominator have no common factors other than 1.

Reducing Fractions to Lowest Terms Let’s look at an example of reducing a fraction to its lowest terms. 6 8 Do 6 and 8 share any factors other than 1? The factors of 6 are 1, 2, 3 and 6. 3 4 The factors of 8 are 1, 2, 4 and 8. The numbers 6 and 8 share a common factor of 2. 6 8 = 3 4 ÷ 2 We can reduce this fraction to its lowest terms by diving both the numerator and the denominator by 2 (the highest common factor). ÷ 2

Reducing Fractions to Lowest Terms As a class, reduce this fraction to its lowest terms. Do 12 and 18 share any factors other than 1? 12 18 The factors of 12 are 1, 2, 3, 4, 6 and 12. 2 3 The factors of 18 are 1, 2, 3, 6, 9 and 18. The numbers 12 and 18 share the common factors of 2, 3 and 6. 12 18 = 2 3 ÷ 6 We can reduce this fraction to its lowest terms by diving both the numerator and the denominator by 6 (the highest common factor). ÷ 6

Lowest Terms - Review Reduce these fractions to their lowest terms by dividing the numerator and denominator by the greatest common factor. 10 15 𝟔 𝟗 8 24

Improper Fractions A proper fraction is a fraction with a value less than one whole. An improper fraction is a fraction with a value greater than one whole. Two halves, five quarters and seven thirds are all examples of improper fractions. To identify whether or not a fraction is improper, there is one simple rule to help you. A fraction is improper if the numerator is equal to or larger than the denominator.

Mixed Numerals 6 3 4 A mixed numeral is a numeral containing both a whole number and a fraction. Two and a half, six and three quarters and ten and two thirds are all examples of mixed numerals. Mixed numerals can be written as improper fractions, and vice versa. mixed numeral 27 4 improper fraction

Converting Improper Fractions Let’s now convert an improper fraction into a mixed numeral. Here are some pizzas, cut into fifths. There are fourteen fifths all together. The improper fraction to represent this is 14 5 . To convert this to a mixed numeral, we need to: 1. Divide the numerator by the denominator. 14 ÷ 5 = 2 r 4 2. Write down the whole number answer. 14 5 =2 4 5 3. Next to the whole number answer, make a fraction by writing down any remainder on top of the original denominator.

Converting Improper Fractions As a class, convert this improper fraction into a mixed numeral. The improper fraction to represent this is 10 3 . To convert this to a mixed numeral, we need to: 1. Divide the numerator by the denominator. 2. Write down the whole number answer. 10 ÷ 3 = 3 r 1 3. Next to the whole number answer, make a fraction by writing down any remainder on top of the original denominator. 10 3 =3 1 3

Converting Mixed Numerals Let’s now convert a mixed numeral to an improper fraction. Here are the same pizzas. There are two and four fifths pizzas all together. The mixed numeral to represent this is 2 4 5 . To convert this to an improper fraction, we need to: 1. Multiply the whole number by the denominator of the fraction. 2 x 5 = 10 2. Add the answer of the multiplication sum to the numerator of the fraction. 10 + 4 = 14 3. The answer becomes the numerator of the fraction, written on top of the original denominator. 2 4 5 = 14 5

Converting Mixed Numerals As a class, convert this mixed numeral into an improper fraction. The mixed numeral to represent this is 3 1 3 . To convert this to an improper fraction, we need to: 1. Multiply the whole number by the denominator of the fraction. 3 x 3 = 9 2. Add the answer of the multiplication sum to the numerator of the fraction. 9 + 1 = 10 3. The answer becomes the numerator of the fraction, written on top of the original denominator. 3 1 3 = 10 3

Converting Fractions - Review Convert these improper fractions to mixed numerals. 1. 23 6 = 2. 43 5 = 3. 22 3 = 4. 49 2 = 5. 68 11 = Convert these mixed numerals to improper fractions. 1. 4 5 6 = 2. 8 3 7 = 3. 6 2 3 = 4. 7 8 9 = 5. 3 1 9 =

Converting Fractions - Answers Convert these improper fractions to mixed numerals. 1. 23 6 = 3 5 6 2. 43 5 =8 3 5 3. 22 3 =7 1 3 4. 49 2 =24 1 2 5. 68 11 =6 2 11 Convert these mixed numerals to improper fractions. 1. 4 5 6 = 29 6 2. 8 3 7 = 59 7 3. 6 2 3 = 20 3 4. 7 8 9 = 71 9 5. 3 1 9 = 28 9