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Whole numbers Multiplying and dividing fractions Multiplying fractionsHere we will learn about fractions of numbers and how to solve problems involving fractions of numbers.
Students first learn about fractions of numbers in fourth grade in their work with number and operations – fractions. They will extend this understanding as they progress through 5th and 6th grade.
Fractions of numbers are calculated when we multiply a fractional number by the whole number. The word โofโ means to multiply.
For example, letโs look at how to use a visual model and the algorithm to calculate fractions of numbers.
How does this relate to 4th grade math?
In order to find a fraction of a number using a model.
In order to find a fraction of a number using the algorithm
Use this worksheet to check your grade 4 studentsโ understanding of fractions of numbers. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your grade 4 studentsโ understanding of fractions of numbers. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREE\cfrac{1}{4} \, of 7
7 or \, \cfrac{7}{1} \, is drawn vertically and \, \cfrac{1}{4} \, is drawn horizontally which is 7 wholes divided into 4 equal pieces.
2Connect the fractions all the way across with 2 different colors.
3Count up the shaded, overlapping parts.
7 groups of \, \cfrac{1}{4} \, represents the overlap shaded pieces which is
\cfrac{1}{4}+\cfrac{1}{4}+\cfrac{1}{4}+\cfrac{1}{4}+\cfrac{1}{4}+\cfrac{1}{4}+\cfrac{1}{4}=\cfrac{7}{4}4If possible, simplify or convert to a mixed number.
There is no common factor between 7 and 4 which means \, \cfrac{7}{4} \, is in its simplest form.
\cfrac{7}{4} \, as a mixed number is 1\cfrac{3}{4}
\cfrac{1}{4} \, of 7=1\cfrac{3}{4}
\cfrac{1}{2} \, of 16
Convert to a multiplication statement.
\cfrac{1}{2} \times 16
Convert the whole number to an improper fraction.
16 as an improper fraction is \, \cfrac{16}{1} .
Multiply the numerators together and the denominators together.
\cfrac{1}{2} \times \cfrac{16}{1}=\cfrac{1 \, \times \, 16}{2 \, \times \, 1}
If possible, simplify or convert to a whole number or mixed number.
\cfrac{16}{2} \, has a common factor of 2 .
\cfrac{16\div 2}{2\div 2}=\cfrac{8}{1} = 8
\cfrac{3}{10} \, of 5
Draw one fraction horizontally and the other vertically.
5 or \cfrac{5}{1} drawn vertically and \cfrac{1}{10} drawn horizontally which is 5 wholes divided into 10 equal pieces.
Connect the fractions all the way across with \bf{2} different colors.
Count up the shaded, overlapping parts.
5 groups of \cfrac{3}{10} \, represent the overlap shaded pieces which is
\cfrac{3}{10}+\cfrac{3}{10}+\cfrac{3}{10}+\cfrac{3}{10}+\cfrac{3}{10}=\cfrac{15}{10}
If possible, simplify or convert to a whole number or mixed number.
The common factor between \cfrac{15}{10} \, is 5.
\cfrac{15 \, \div \, 5}{10 \, \div \, 5}=\cfrac{3}{2}=1\cfrac{1}{2}
Find \, \cfrac{2}{7} \, of 28 .
Convert to a multiplication statement.
\cfrac{2}{7} \times 28
Convert the whole number to an improper fraction.
\cfrac{2}{7}\times \cfrac{28}{1}
Multiply the numerators together and the denominators together.
\cfrac{2}{7}\times \cfrac{28}{1} = \cfrac{2 \, \times \, 28}{7 \, \times \, 1}=\cfrac{56}{7}
If possible, simplify or convert to a whole number or mixed number.
The common factor between \, \cfrac{56}{7} \, is 7.
\cfrac{56 \, \div \, 7}{7 \, \div \, 7}=\cfrac{8}{1}=8
\cfrac{2}{7} \, of 28 is 8 .
What is \, \cfrac{3}{4} \, of 20?
Convert to a multiplication statement.
\cfrac{3}{4}\times 20
Convert the whole number to an improper fraction.
\cfrac{3}{4}\times \cfrac{20}{1}
Multiply the numerators together and the denominators together.
\cfrac{3}{4}\times \cfrac{20}{1}= \cfrac{3\times 20}{4\times1}= \cfrac{60}{4}
If possible, simplify or convert to a whole number or mixed number.
The common factor between 4 and 60 is 4.
\cfrac{60 \, \div \, 4}{4 \, \div \, 4}=\cfrac{15}{1}=15
\cfrac{3}{4} \, of 20 is 15 .
Jenny went hiking and only walked two thirds of the 24 mile hiking trail. How many miles did she hike?
Convert to a multiplication statement.
\cfrac{2}{3} \, of 24 is \, \cfrac{2}{3} \times 24
Convert the whole number to an improper fraction.
\cfrac{2}{3} \times\cfrac{24}{1}
Multiply the numerators together and the denominators together.
\cfrac{2}{3} \times\cfrac{24}{1} = \cfrac{2 \, \times \, 24}{3 \, \times \, 1} =\cfrac{48}{3}
If possible, simplify or convert to a whole number or mixed number.
The common factor between 48 and 3 is 3.
\cfrac{48 \, \div \, 3}{3 \, \div \, 3}=\cfrac{16}{1}=16
Two thirds of 24 is 16, so she hiked 16 miles.
Dylan only filled \, \cfrac{2}{5} \, of his 20 -ounce water bottle. How much water is there in the bottle?
Convert to a multiplication statement.
\cfrac{2}{5}\times 20
Convert the whole number to an improper fraction.
\cfrac{2}{5}\times \cfrac{20}{1}
Multiply the numerators together and the denominators together.
\cfrac{2}{5}\times \cfrac{20}{1}=\cfrac{2 \, \times \, 20}{5 \, \times \, 1}=\cfrac{40}{5}
If possible, simplify or convert to a whole number or mixed number.
The common factor between 40 and 5 is 5.
\cfrac{40 \, \div \, 5}{5 \, \div \, 5}= \cfrac{8}{1}= 8
\cfrac{2}{5} \, of 20 is 8, so there are 8 ounces of water in the bottle.
1. Find \, \cfrac{1}{3} \, of 9
To use a model to find the answer:
9 or \, \cfrac{9}{1} \, is vertical and \, \cfrac{1}{3} \, is horizontal which is 9 divided into 3 equal pieces.
The overlap shaded region represents 9 groups of \, \cfrac{1}{3} \, or
\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}+\cfrac{1}{3}=\cfrac{9}{3}
\cfrac{9}{3} = 3
\cfrac{1}{3} \, of 9 is 3
2. Find \, \cfrac{1}{2} \, of 18
\cfrac{1}{2} \, of 18 is \, \cfrac{1}{2} \times 18
18 as an improper fraction is \, \cfrac{18}{1}
So, \cfrac{1}{2}\times\cfrac{18}{1}=\cfrac{18}{2}
The common factor of 18 and 2 is 2
\cfrac{18 \, \div \, 2}{2 \, \div \, 2}=\cfrac{9}{1}=9
\cfrac{1}{2} \, of 18 is 9
3. Find \, \cfrac{3}{4} \, of 8
To use a model to find the answer:
\cfrac{8}{1} \, is horizontal and \, \cfrac{3}{4} \, is vertical.
The overlap shaded region represents 8 groups of \, \cfrac{3}{4} \, or
\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}+\cfrac{3}{4}=\cfrac{24}{4}
\cfrac{24}{4}=6
4. Find \, \cfrac{5}{8} \, of 56
\cfrac{5}{8} \, of 56 is \, \cfrac{5}{8}\times 56
56 as an improper fraction is \, \cfrac{56}{1}
So, \, \cfrac{5}{8}\times\cfrac{56}{1}=\cfrac{5 \, \times \, 56}{8 \, \times \, 1}= \cfrac{280}{8}
The common factor of 280 and 8 is 8.
\cfrac{280 \, \div \, 8}{8 \, \div \, 8}=\cfrac{35}{1}=35
\cfrac{5}{8} \, of 56 is 35
5. Lucas ran \, \cfrac{1}{5} \, of a 15 mile running path. How far did he run?
7.5 miles
4 miles
10 miles
3 miles
\cfrac{1}{5} \, of 15 is \, \cfrac{1}{5}\times 15
15 as an improper fraction is \, \cfrac{15}{1}
So, \, \cfrac{1}{5}\times\cfrac{15}{1}=\cfrac{1 \, \times \, 15}{5 \, \times \, 1}= \cfrac{15}{5}
The common factor between 15 and 5 is 5.
\cfrac{15 \, \div \, 5}{5 \, \div \, 5}=\cfrac{3}{1}=3
\cfrac{1}{5} \, of 15 is 3
6. Maddie reads four-fifths of the 65 pages of her book. How many pages did she read?
52 pages
13 pages
48 pages
54 pages
\cfrac{4}{5} \, of 65 is \, \cfrac{4}{5}\times 65
65 as an improper fraction is \, \cfrac{65}{1}
\cfrac{4}{5}\times \cfrac{65}{1}=\cfrac{4 \, \times \, 65}{5 \, \times \, 1}=\cfrac{260}{5}
The common factor between 260 and 5 is 5.
\cfrac{260 \, \div \, 5}{5 \, \div \, 5}=\cfrac{52}{1} =52
\cfrac{4}{5} \, of 65 is 52 pages
Yes, the word โofโ means to multiply. So finding the fraction of a number is the same as when you multiply fractions.
Yes, in order to make a whole number a fraction, place it over 1. So the denominator of the fraction is always 1.
Mixed fractions and mixed numbers mean the same thing.
You can get a common denominator to multiply fractions, but it isnโt necessary for multiplication.
There are proper fractions where the numerator (top number) is smaller than the denominator (bottom number). There are unit fractions where the numerator (top number) is 1 and the denominator (bottom number) is a whole number. There are improper fractions where the numerator (top number) is greater than the denominator (bottom number). There are mixed numbers or mixed fractions that are made up of a whole number and a proper fraction.
They are similar because they can have a whole part and a fractional part.
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