Find the value of each of the following. Leave each answer as a mixed number in its simplest form where applicable.
(a) [tex]$10 \frac{3}{5}-3 \frac{1}{5}$[/tex]
(b) [tex]$2 \frac{3}{7}-\frac{4}{7}$[/tex]
(c) [tex]$\frac{37}{18}-1 \frac{7}{18}$[/tex]
(d) [tex]$2 \frac{8}{11}-2 \frac{9}{22}$[/tex]
(e) [tex]$10 \frac{3}{8}-6 \frac{13}{24}$[/tex]
(f) [tex]$\frac{15}{4}-2 \frac{1}{6}$[/tex]
(g) [tex]$3 \frac{5}{8}-1 \frac{5}{6}$[/tex]
(h) [tex]$3 \frac{5}{7}-\frac{7}{5}$[/tex]
Answer (2)
By breaking down each subtraction problem into whole numbers and fractions, we properly calculated the answers for mixed numbers and improper fractions. We simplified fractions when necessary and presented the final answers as mixed numbers in simplest form. The results illustrate the process of subtraction in a straightforward manner.
;
Subtract the whole numbers and fractions separately for (a).
Borrow 1 from the whole number when the fraction being subtracted is larger for (b), (e), and (g).
Convert mixed numbers to improper fractions and subtract for (c), (f), and (h).
Find a common denominator before subtracting fractions.
Simplify the resulting fraction to its simplest form.
The final answers are:
(a) 7 5 2
(b) 1 7 6
(c) 3 2
(d) 22 7
(e) 3 6 5
(f) 1 12 7
(g) 1 24 19
(h) 2 35 11
Explanation
Understanding the Problem We need to find the value of each expression and leave the answer as a mixed number in its simplest form where applicable.
Solving (a) (a) Subtract the whole numbers and fractions separately: 10 5 3 − 3 5 1 = ( 10 − 3 ) + ( 5 3 − 5 1 ) = 7 + 5 2 = 7 5 2
Solving (b) (b) Since the fraction being subtracted is larger than the first fraction, borrow 1 from the whole number: 2 7 3 − 7 4 = 1 + 7 7 + 3 − 7 4 = 1 + 7 10 − 7 4 = 1 + 7 6 = 1 7 6
Solving (c) (c) Convert the mixed number to an improper fraction and then subtract: 18 37 − 1 18 7 = 18 37 − 18 18 + 7 = 18 37 − 18 25 = 18 12 = 3 2
Solving (d) (d) Find a common denominator and then subtract: 2 11 8 − 2 22 9 = 2 22 16 − 2 22 9 = ( 2 − 2 ) + ( 22 16 − 22 9 ) = 0 + 22 7 = 22 7
Solving (e) (e) Find a common denominator and then subtract: 10 8 3 − 6 24 13 = 10 24 9 − 6 24 13 . Borrow 1 from the whole number: 10 24 9 − 6 24 13 = 9 + 24 24 + 9 − 6 24 13 = 9 24 33 − 6 24 13 = ( 9 − 6 ) + ( 24 33 − 24 13 ) = 3 + 24 20 = 3 6 5
Solving (f) (f) Convert the mixed number to an improper fraction and then subtract: 4 15 − 2 6 1 = 4 15 − 6 12 + 1 = 4 15 − 6 13 . Find a common denominator: 4 15 − 6 13 = 12 45 − 12 26 = 12 19 = 1 12 7
Solving (g) (g) Find a common denominator and then subtract: 3 8 5 − 1 6 5 = 3 24 15 − 1 24 20 . Borrow 1 from the whole number: 3 24 15 − 1 24 20 = 2 + 24 24 + 15 − 1 24 20 = 2 24 39 − 1 24 20 = ( 2 − 1 ) + ( 24 39 − 24 20 ) = 1 + 24 19 = 1 24 19
Solving (h) (h) Convert the mixed number to an improper fraction and then subtract: 3 7 5 − 5 7 = 7 21 + 5 − 5 7 = 7 26 − 5 7 . Find a common denominator: 7 26 − 5 7 = 35 130 − 35 49 = 35 81 = 2 35 11
Final Answer The values of the expressions are: (a) 7 5 2 (b) 1 7 6 (c) 3 2 (d) 22 7 (e) 3 6 5 (f) 1 12 7 (g) 1 24 19 (h) 2 35 11
Examples
Understanding how to subtract mixed numbers is very useful in everyday life. For example, if you are baking a cake and the recipe calls for 3 4 1 cups of flour, but you only have 1 2 1 cups, you need to calculate how much more flour you need. This involves subtracting mixed numbers: 3 4 1 − 1 2 1 . Knowing how to perform this subtraction allows you to accurately measure the additional flour required, ensuring your cake turns out perfectly. This skill is also helpful when measuring ingredients for other recipes, calculating distances, or managing time.
