2.03 Adding and subtracting fractions
Simplify:
State the lowest common denominator of the following sets of fractions:
\dfrac{1}{3}, \, \dfrac{1}{2}
\dfrac{1}{4}, \, \dfrac{1}{9}
\dfrac{1}{2}, \, \dfrac{1}{4}, \, \dfrac{2}{5}
\dfrac{5}{12}, \, \dfrac{1}{6}, \, \dfrac{2}{3}
Complete the following statements:
| \displaystyle \frac{2}{3} + \frac{1}{9} | \displaystyle = | \displaystyle \frac{6}{⬚} + \frac{1}{⬚} | Rewrite with a common denominator |
| \displaystyle = | \displaystyle \dfrac{7}{⬚} | Evaluate the sum |
| \displaystyle \frac{1}{2} + \frac{2}{3} | \displaystyle = | \displaystyle \frac{⬚}{6} + \frac{⬚}{6} | Rewrite with a common denominator |
| \displaystyle = | \displaystyle \frac{⬚}{6} | Evaluate the sum | |
| \displaystyle = | \displaystyle 1 \frac{⬚}{6} | Rewrite as a mixed number |
| \displaystyle \frac{7}{8} - \frac{3}{16} | \displaystyle = | \displaystyle \frac{⬚}{⬚} - \frac{3}{⬚} | Rewrite with a common denominator |
| \displaystyle = | \displaystyle \frac{⬚}{⬚} | Evaluate the difference |
| \displaystyle \frac{11}{4} - \frac{7}{6} | \displaystyle = | \displaystyle \frac{⬚}{⬚} - \frac{⬚}{⬚} | Rewrite with a common denominator |
| \displaystyle = | \displaystyle \frac{19}{⬚} | Evaluate the difference | |
| \displaystyle = | \displaystyle 1 \frac{⬚}{⬚} | Rewrite as a mixed number |
Simplify the following, writing your answer as a mixed number where necessary:
Consider the expression 2 \dfrac{1}{4} + 5 \dfrac{1}{2}.
Find the sum of the whole number part of each mixed number.
Find the sum of the fraction part of each mixed number.
Simplify 2 \dfrac{1}{4} + 5 \dfrac{1}{2}.
Fill in the boxes to complete the working out:
| \displaystyle 1 \frac{1}{4} + 2 \frac{2}{4} | \displaystyle = | \displaystyle 1 + ⬚ + \frac{1}{⬚} + \frac{2}{⬚} | Group the whole number parts and fraction parts |
| \displaystyle = | \displaystyle ⬚ + \frac{⬚}{⬚} | Add the whole number parts and fraction parts | |
| \displaystyle = | \displaystyle ⬚ \frac{⬚}{⬚} | Evaluate the sum |
Consider the expression 3 \dfrac{1}{3} - 2 \dfrac{1}{6}.
Rewrite the mixed numbers as improper fractions.
Using part (a), rewrite the improper fractions with the same denominator.
Simplify 3 \dfrac{1}{3} - 2 \dfrac{1}{6}.
Fill in the boxes to complete the working out:
| \displaystyle 2 \frac{1}{3} - 1 \frac{5}{9} | \displaystyle = | \displaystyle \frac{⬚}{3} - \frac{⬚}{9} | Rewrite as improper fractions |
| \displaystyle = | \displaystyle \frac{⬚}{⬚} - \frac{⬚}{9} | Rewrite with a common denominator | |
| \displaystyle = | \displaystyle \frac{⬚}{⬚} | Evaluate the difference |
Simplify the following, writing your answer as a mixed number where necessary:
Simplify the following, writing your answer as a mixed number where necessary:
Marge ran three ninths of a kilometre. She took a 5-minute rest, then ran another three thirds of a kilometre. How many kilometres did she run in total?
Jack felt dehydrated. He drank one third of a litre at first, then drank another one ninth of a litre. How many litres did he drink in total?
Valerie walks eight sixths of a kilometre to school while Fred walks one half of a kilometre to school. How much farther does Valerie walk than Fred?
A bridge is being built to span \dfrac{3}{4} \text{ km}. After a month, the engineer reported that \dfrac{3}{8} \text{ km} has been completed so far. What part of the bridge has not yet been completed?
Jane eats \dfrac{1}{4} of a cake and Joshua eats \dfrac{1}{3} of the cake. What fraction of the cake did they eat altogether?
During a blizzard it snowed 10\dfrac{1}{2} \text{ cm}. When the sun came out the next day, 5 \dfrac{3}{4} \text{ cm} of show melted. How much snow was left on the ground?
A market stall is open for 3 \dfrac{1}{2} hours in the morning and 2 \dfrac{3}{4} hours in the evening. How many hours is the stall open altogether?
Georgio buys 3 cups of sugar to use in his baking. He uses \dfrac{3}{4} of a cup in his cake, 1 \dfrac{1}{5} of a cup in his pastries and accidentally spilled \dfrac{1}{2} of a cup. How much sugar does he have left?
Mr. Pemberton, the president of Zoom Motors, owns \dfrac{1}{3} of the stock of the company. His wife owns \dfrac{1}{4} of the stock. What fractional part of the stock will his daughter need to purchase in order for the family to own \dfrac{3}{4} of the stock?
Missy mailed 4 letters that have a total weight of 3 grams. One letter weighed \dfrac{1}{2} of a gram, another weighed \dfrac{3}{4} of a gram, and a third weighed \dfrac{7}{8} of a gram. How much did the fourth letter weigh?