What is 5/7 minus 4 1/2?

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What is 5/7 minus 4 1/2?

Answer

5/7 minus 4 1/2 is
-53/14

4 1/2 is larger than 5/7, so the answer is below zero.

As a mixed number: -3 11/14

As a decimal: ≈ -3.7857

5
7
-
4
1
2
=
-
53
14

-53/14 is what is left when 4 1/2 is taken away from 5/7. As a mixed number that is -3 11/14.

Steps to subtract 4 1/2 from 5/7

Only parts of the same size can be taken away from each other, so 5/7 - 4 1/2 is solved by giving both fractions the same denominator and then subtracting the numerators. Here is every step.

Step 1: Write both numbers as fractions

A whole number is written over 1, and a mixed number becomes an improper fraction: multiply the whole part by the denominator and add the numerator.

4 1/2 = (4 × 2 + 1)/2 = 9/2

Step 2: Find the common denominator

The least common multiple of 7 and 2 is 14, so both fractions are rewritten over it.

5/7 = 10/14 (× 2)

9/2 = 63/14 (× 7)

Step 3: Subtract the numerators

The denominator stays as it is — it says how big each part is, and that has not changed. Only the count of parts is subtracted.

10/14 - 63/14

=

(10 - 63)/14

=

-53/14

The second numerator is the larger one, so the subtraction goes past zero and the answer keeps a minus sign. The other order, 4 1/2 - 5/7, gives the same size with the opposite sign: 53/14.

Step 4: Write it as a mixed number

The numerator is larger than the denominator, so -53/14 can also be written as a mixed number.

-53/14 = -3 11/14

Answer

5/7 - 4 1/2

=

-53/14

(-3 11/14)

As a decimal, 5/7 - 4 1/2 ≈ -3.7857 — the decimal form is rounded, the fraction -53/14 is the exact answer.

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Subtracting Fractions Calculator

This calculator subtracts one fraction from another and shows the whole solution, not just the answer. Mixed numbers and whole numbers are accepted on both sides, so you can take 1/2 away from 2 1/3 just as easily as from 3/4.

For example, it can help you find out what is 5/7 minus 4 1/2? (The answer is: -53/14).

Enter the number you start from on the left and the number you take away on the right (for example '5/7' and '4 1/2'), then press the button.

Order matters here: 1/2 - 1/3 and 1/3 - 1/2 are different questions. When the second number is the larger one the answer is negative, and the page prints the minus sign instead of hiding it.

Every page also shows why the method works: only parts of the same size can be taken away from each other, so both fractions are first rewritten over their least common denominator and only then are the numerators subtracted.

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Fraction Subtraction Table

SubtractionResultDecimal Form
5/7 - 1 1/3-13/21≈ -0.619
5/7 - 1 1/2-11/14≈ -0.7857
5/7 - 3/2-11/14≈ -0.7857
5/7 - 1 2/3-20/21≈ -0.9524
5/7 - 5/3-20/21≈ -0.9524
5/7 - 1 3/4-29/28≈ -1.0357
5/7 - 2-9/7≈ -1.2857
5/7 - 2 1/4-43/28≈ -1.5357
5/7 - 2 1/3-34/21≈ -1.619
5/7 - 2 1/2-25/14≈ -1.7857
5/7 - 2 2/3-41/21≈ -1.9524
5/7 - 2 3/4-57/28≈ -2.0357
5/7 - 3-16/7≈ -2.2857
5/7 - 3 1/4-71/28≈ -2.5357
5/7 - 3 1/3-55/21≈ -2.619
5/7 - 3 1/2-39/14≈ -2.7857
5/7 - 3 3/4-85/28≈ -3.0357
5/7 - 4-23/7≈ -3.2857
5/7 - 4 1/2-53/14≈ -3.7857
5/7 - 5 2/3-104/21≈ -4.9524

FAQ

What is 5/7 minus 4 1/2?

5/7 minus 4 1/2 is -53/14

How do you subtract 4 1/2 from 5/7?

The least common denominator of 5/7 and 9/2 is 14. The difference is then 10/14 - 63/14 = -53/14, already in lowest terms.

What is 5/7 minus 4 1/2 as a decimal?

The exact answer is the fraction -53/14; its decimal form is rounded here, so 5/7 - 4 1/2 ≈ -3.7857.

Why is 5/7 minus 4 1/2 negative?

4 1/2 is larger than 5/7, so taking it away goes past zero and the answer is -53/14. The other order, 4 1/2 - 5/7, has the same size and the opposite sign: 53/14.

See Also