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Numerator and denominator Equivalent fractions Improper fraction to mixed number Mixed number to improper fractionHere you will learn about how to subtract fractions with like denominators and with unlike denominators. You will also learn how to subtract mixed numbers.
Students will first learn about subtracting fractions as part of number and operations in fractions in elementary school.
Subtracting fractions is when you subtract two or more fractions to find the difference.
To do this, fractions need a common denominator (bottom number). Then you can subtract the fractions by subtracting the numerators (top numbers).
For example,
\cfrac{7}{8}-\cfrac{3}{8}=
Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left, 7-4=3.
There are 3 parts. But what size are the parts? They are still eighths, so the denominator stays the same.
\cfrac{7}{8}-\cfrac{4}{8}=\cfrac{3}{8}
If the denominators are not the same, you create equivalent fractions before adding.
For example,
\cfrac{2}{3}-\cfrac{5}{9}=
The equation is taking \cfrac{5}{9} away from \cfrac{2}{3}.
Since the denominators are NOT the same, the parts are NOT the same size. Use equivalent fractions to create a common denominator of 9.
Multiply the numerator and denominator of \cfrac{2}{3} by 3.
\cfrac{2 \; \times \; 3}{3 \; \times \; 3}=\cfrac{6}{9}
Now use the equivalent fraction to work out \cfrac{6}{9}-\cfrac{5}{9}.
You subtract to see how many parts are left, 6-5=1.
There is 1 part. But what size is the part? It is still a ninth, so the denominator stays the same.
\cfrac{6}{9}-\cfrac{5}{9}=\cfrac{1}{9}
How does this relate to 4th grade math and 5th grade math?
In order to subtract fractions with like denominators:
In order to subtract mixed numbers with like denominators:
In order to subtract fractions with unlike denominators:
In order to subtract mixed numbers with unlike denominators:
Use this quiz to check your grade 4 to 6 studentsβ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 4 to 6 studentsβ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!
DOWNLOAD FREESolve \cfrac{3}{5}-\cfrac{1}{5}.
The equation is taking \cfrac{1}{5} away from \cfrac{3}{5}.
Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 3-1=2.
2Write your answer as a fraction.
There are 2 parts. But what size are the parts? They are still fifths, so the denominator stays the same.
\cfrac{3}{5}-\cfrac{1}{5}=\cfrac{2}{5}
Solve 4 \cfrac{11}{12}-1 \cfrac{7}{12}.
Subtract the fractions, borrowing if needed.
The equation is taking 1 \cfrac{7}{12} away from 4 \cfrac{11}{12}.
Start with the fractions. Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 11-7=4.
There are 4 parts. But what size are the parts? They are still twelfths, so the denominator stays the same.
\cfrac{11}{12}-\cfrac{7}{12}=\cfrac{4}{12}
Subtract the whole numbers.
4-1=3
Write your answer as a mixed number.
4 \cfrac{11}{12}-1 \cfrac{7}{12}=3 \cfrac{4}{12}
You can also write this answer as the equivalent fraction 3 \cfrac{1}{3}.
Solve 2 \cfrac{3}{10}-1 \cfrac{9}{10}.
Subtract the fractions, borrowing if needed.
The equation is taking 1 \cfrac{9}{10} away from 2 \cfrac{3}{10}.
Start with the fractions. Since the denominators are the same, the parts are the same size. However, there are not enough parts to take 9 away from 3.
You can break one of the wholes into \cfrac{10}{10} …
2 \cfrac{3}{10}=1 \cfrac{13}{10}
Now you can solve 1 \cfrac{13}{10}-1 \cfrac{9}{10}.
You subtract to see how many parts are left: 13-9=4.
There are 4 parts. But what size are the parts? They are still tenths, so the denominator stays the same.
\cfrac{13}{10}-\cfrac{9}{10}=\cfrac{4}{10}
Subtract the whole numbers.
1-1=0
Write your answer as a mixed number.
Sometimes the answer will be just a fraction.
1 \cfrac{13}{10}-1 \cfrac{9}{10}=\cfrac{4}{10}
You can also write this answer as the equivalent fraction \cfrac{2}{5} or the decimal 0.4.
Solve \cfrac{3}{4}-\cfrac{1}{2}.
Create common denominators (bottom numbers).
Since \cfrac{3}{4} and \cfrac{1}{2} do not have like denominators, the parts are NOT the same size. A common denominator of 4 can be used.
Multiply the numerator and denominator of \cfrac{1}{2} by 2 to create an equivalent fraction.
\cfrac{3}{4} \quad and \quad \cfrac{1 \; \times \; 2}{2 \; \times \; 2}=\cfrac{2}{4}
Subtract the numerators (top numbers).
Now use the equivalent fraction to solve: \cfrac{3}{4}-\cfrac{2}{4}.
Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 3-2=1.
Write your answer as a fraction.
There is 1 part. But what size is the part? It is still a fourth, so the denominator stays the same.
\cfrac{3}{4}-\cfrac{2}{4}=\cfrac{1}{4}
Solve 2 \cfrac{1}{2}-1 \cfrac{1}{3}.
Create common denominators (bottom numbers).
The equation is taking 1 \cfrac{1}{3} away from 2 \cfrac{1}{2}.
Start with the fractions. Since \cfrac{1}{2} and \cfrac{1}{3} do not have like denominators, the parts are NOT the same size.
Multiply the numerator and denominator by the opposite denominator to create equivalent fractions with common denominators.
\cfrac{1 \; \times \; 3}{2 \; \times \; 3}=\cfrac{3}{6} \quad and \quad \cfrac{1 \; \times \; 2}{3 \; \times \; 2}=\cfrac{2}{6}
Subtract the fractions, borrowing if needed.
Now use the equivalent fractions to solve: 2 \cfrac{3}{6}-1 \cfrac{2}{6}.
Start with the fractions. Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 3-2=1.
There is 1 part. But what size is the part? It is still a sixth, so the denominator stays the same.
\cfrac{3}{6}-\cfrac{2}{6}=\cfrac{1}{6}
Subtract the whole numbers.
2-1=1
Write your answer as a mixed number.
2 \cfrac{3}{6}-1 \cfrac{2}{6}=1 \cfrac{1}{6}
Solve 5 \cfrac{3}{8}-1 \cfrac{3}{4}.
Create common denominators (bottom numbers).
The equation is taking 1 \cfrac{3}{4} away from 5 \cfrac{3}{8}.
Start with the fractions. Since \cfrac{3}{8} and \cfrac{3}{4} do not have like denominators, the parts are NOT the same size. A common denominator of 8 can be used.
Multiply the numerator and denominator of \cfrac{3}{4} by 2 to create an equivalent fraction.
\cfrac{3}{8} \quad and \quad \cfrac{3 \; \times \; 2}{4 \; \times \; 2}=\cfrac{6}{8}
Subtract the fractions, borrowing if needed.
Now use the equivalent fractions to solve: 5 \cfrac{3}{8}-1 \cfrac{6}{8}.
Start with the fractions. Since the denominators are the same, the parts are the same size. However, there are not enough parts to take 6 away from 3.
You can break one of the wholes into \cfrac{8}{8}β¦
5 \cfrac{3}{8}=4 \cfrac{11}{8}
Now you can solve 4 \cfrac{11}{8}-1 \cfrac{6}{8}.
You subtract to see how many parts are left: 11-6=5.
There are 5 parts left. But what size are the parts? They are still eighths, so the denominator stays the same.
\cfrac{11}{8}-\cfrac{6}{8}=\cfrac{5}{8}
Subtract the whole numbers.
4-1=3
Write your answer as a mixed number.
4 \cfrac{11}{8}-1 \cfrac{6}{8}=3 \cfrac{5}{8}
1. Solve \cfrac{5}{6}-\cfrac{2}{6}.
The equation is taking \cfrac{2}{6} away from \cfrac{5}{6}.
Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 5-2=3.
There are 3 parts. But what size are the parts? They are still sixths, so the denominator stays the same.
\cfrac{5}{6}-\cfrac{2}{6}=\cfrac{3}{6}
You can also write this answer as the equivalent fraction \cfrac{1}{2}.
2. Solve 3 \cfrac{1}{4}-1 \cfrac{3}{4}.
The equation is taking 1 \cfrac{3}{4} away from 3 \cfrac{1}{4}.
Start with the fractions. Since the denominators are the same, the parts are the same size. However, there are not enough parts to take 3 away from 1.
You can break one of the wholes into \cfrac{4}{4}β¦
3 \cfrac{1}{4}=2 \cfrac{5}{4}
Now you can solve 2 \cfrac{5}{4}-1 \cfrac{3}{4}.
You subtract to see how many parts are left: 5-3=2.
There are 2 parts. But what size are the parts? They are still fourths, so the denominator stays the same.
\cfrac{5}{4}-\cfrac{3}{4}=\cfrac{2}{4}
Subtract the whole numbers.
2-1=1
2 \cfrac{5}{4}-1 \cfrac{3}{4}=1 \cfrac{2}{4}
You can also write this answer as the equivalent mixed number 1 \cfrac{1}{2}.
3. Solve 4 \cfrac{8}{10}-2 \cfrac{1}{10}.
The equation is taking 2 \cfrac{1}{10} away from 4 \cfrac{8}{10}.
Start with the fractions. Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 8-1=7.
There are 7 parts. But what size are the parts? They are still tenths, so the denominator stays the same.
\cfrac{8}{10}-\cfrac{1}{10}=\cfrac{7}{10}
Subtract the whole numbers.
4-2=2
4 \cfrac{8}{10}-2 \cfrac{1}{10}=2 \cfrac{7}{10}
You can also write this answer as the decimal number 2.7.
4. Solve \cfrac{2}{3}-\cfrac{1}{5}.
Since \cfrac{2}{3} and \cfrac{1}{5} do not have like denominators, the parts are NOT the same size.
Multiply the numerator and denominator by the opposite denominator to create equivalent fractions with common denominators.
\cfrac{2 \; \times \; 5}{3 \; \times \; 5}=\cfrac{10}{15} \quad and \quad \cfrac{1 \; \times \; 3}{5 \; \times \; 3}=\cfrac{3}{15}
Now use the equivalent fractions to solve: \cfrac{10}{15}-\cfrac{3}{15}.
Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 10-3=7.
There are 7 parts. But what size are the parts? They are still fifteenths, so the denominator stays the same.
\cfrac{10}{15}-\cfrac{3}{15}=\cfrac{7}{15}
5. Solve 3\cfrac{3}{4}-2\cfrac{1}{3}.
The equation is taking 2\cfrac{1}{3} away from 3\cfrac{3}{4}.
Start with the fractions. Since \cfrac{3}{4} and \cfrac{1}{3} do not have like denominators, the parts are NOT the same size.
Multiply the numerator and denominator by the opposite denominator to create equivalent fractions with common denominators.
\cfrac{3 \; \times \; 3}{4 \; \times \; 3}=\cfrac{9}{12} \quad and \quad \cfrac{1 \; \times \; 4}{3 \; \times \; 4}=\cfrac{4}{12}
Now use the equivalent fractions to solve: 3 \cfrac{9}{12}-2 \cfrac{4}{12}.
Start with the fractions. Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 9-4=5.
There are 5 parts. But what size are the parts? They are still twelfths, so the denominator stays the same.
\cfrac{9}{12}-\cfrac{4}{12}=\cfrac{5}{12}
Subtract the whole numbers.
3-2=1
3 \cfrac{9}{12}-2 \cfrac{4}{12}=1 \cfrac{5}{12}
6. Solve 5 \cfrac{1}{12}-3 \cfrac{5}{6}.
The equation is taking 3 \cfrac{5}{6} away from 5 \cfrac{1}{12}.
Start with the fractions. Since \cfrac{1}{12} and \cfrac{5}{6} do not have like denominators, the parts are NOT the same size. A common denominator of 12 can be used.
Multiply the numerator and denominator of \cfrac{5}{6} by 2 to create an equivalent fraction.
\cfrac{1}{12} \quad and \quad \cfrac{5 \; \times \; 2}{6 \; \times \; 2}=\cfrac{10}{12}
Now use the equivalent fraction to solve: 5 \cfrac{1}{12}-3 \cfrac{10}{12}.
Start with the fractions. Since the denominators are the same, the parts are the same size. However, there are not enough parts to take 10 away from 1.
You can break one of the wholes into \cfrac{12}{12}β¦
5 \cfrac{1}{12}=4 \cfrac{13}{12}
Now you can solve 4 \cfrac{13}{12}-3 \cfrac{10}{12}.
You subtract to see how many parts are left: 13-10=3.
There are 3 parts left. But what size are the parts? They are still twelfths, so the denominator stays the same.
\cfrac{13}{12}-\cfrac{10}{12}=\cfrac{3}{12}
Subtract the whole numbers.
4-3=1
4 \cfrac{13}{12}-3 \cfrac{10}{12}=1 \cfrac{3}{12}
You can also write this answer as the equivalent mixed number 1 \cfrac{1}{4}.
No, although a new numerator and new denominator are created the value of the fraction remains the same. Since the new fraction has a larger denominator, the parts will be smaller, so the numerator also needs to be larger so that the total of the parts is the same size as the original fraction.
No, students do not have to find the least common denominator in order to correctly answer a fraction addition question. However, as students progress in their understanding of fractions, it is a good habit to grow. It is also important to be mindful of standard expectations, as they may vary from state to state.
Yes, you follow many of the same steps to add fractions, which also requires common denominators. The only difference is that you add the numerators instead of subtracting.
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