4.3 Extending Operations to Fractions

What fraction of the rectangle is shaded? Explain how you know.

1. Locate and label \(\frac{3}{4}\) and \(\frac{6}{4}\) on the number line.

   

   

2. Explain why your points represent \(\frac{3}{4}\) and \(\frac{6}{4}\).

Write a multiplication expression for each image. Explain your reasoning.

1.  

   

   

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2.  

   

   

Here are the lengths of some lizards in inches. Use the lengths to complete the line plot.

Write an expression that matches each diagram. Then, find the value of each expression.

Five friends go on a hike. They each bring \(\frac{1}{4}\) cup of nuts.

1. If the shaded parts represent the amount of nuts the friends bring on their hike, which diagram matches the story? Explain your reasoning.

   A

   

   B

   

2. How many cups of nuts do the friends bring on the hike?

Kiran’s cat eats \(\frac{1}{2}\) cup of food each day.

1. How much food does Kiran’s cat eat in a week?
2. Draw a diagram to represent the situation.

1. Draw a diagram to show \(3 \times \frac{7}{8}\).
2. How does the diagram help you find the value of the expression \(3 \times \frac{7}{8}\)?

Each bead weighs \(\frac{5}{8}\) gram. How much do 7 beads weigh? Explain or show your reasoning.

1. Measure how thick your workbook is to the nearest \(\frac{1}{8}\) inch.
2. If all of your classmates stacked their workbooks together, how tall would the stack be? Explain or show your reasoning.
3. Check your answer by measuring, if possible.

Diego walked the same number of miles to school each day. He says that he walked \(\frac{48}{5}\) miles in total, but does not say how many days that distance includes.

What are some possible number of days Diego counted and the distance he walked each of those days?

1. Write \(\frac{4}{3}\) in as many ways as you can as a sum of fractions.
2. Write \(\frac{9}{8}\) in at least 3 different ways as a sum of fractions.

1. Draw “jumps” on the number lines to show two ways to use fourths to make a sum of \(\frac{7}{4}\).

   

   

   

   

2. Represent each combination of jumps as an equation.

1. 

   

   Explain how the diagram represents \(\frac{13}{5} - \frac{4}{5}\).

   Use the diagram to find the value of \(\frac{13}{5}- \frac{4}{5}\).

2. Use a number line to represent and find the difference \(\frac{9}{4} - \frac{3}{4}\).

   

   

Show two different ways to find the difference: \(2 - \frac{3}{4}\)

Elena is making friendship necklaces and wants the chain and clasp to be a total of \(18\frac{1}{4}\) inches long. She is going to use a clasp that is \(2\frac{3}{4}\) inches long. How long does her chain need to be? Explain or show your reasoning.

For each of the expressions, explain whether you think it would be helpful to decompose one or more numbers to find the value of the expression.

1. \(\frac{4}{3} + \frac{5}{3}\)
2. \(5\frac{1}{5} - 2\frac{2}{5}\)
3. \(9\frac{5}{6} - 6\frac{1}{6}\)

The lengths of the shoes of a dad and his two daughters are shown.

For each question, show your reasoning.

1. How much longer is the older daughter’s shoes than her sister’s?
2. Which is longer, the dad’s shoes or the combined lengths of his daughters’ shoes?

A chocolate chip cookie recipe calls for \(2\frac{3}{4}\) cups of flour. You only have a \(\frac{1}{4}\)-cup measuring cup and a \(\frac{3}{4}\)-cup measuring cup that you can use. 

1. What are different combinations of the measuring cups that you can use to get a total of \(2\frac{3}{4}\) cups of flour?
2. Write each of the combinations as an addition equation.

The table shows some lengths of different shoe sizes in inches.

Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: \(\frac{1}{2}\)-foot, \(\frac{1}{4}\)-foot, and \(\frac{1}{8}\)-foot. 

Andre stacks two \(\frac{1}{2}\)-foot blocks, two \(\frac{1}{4}\)-foot blocks, and two \(\frac{1}{8}\)-foot blocks to create a tower. What will the height of the tower be in feet? Explain or show how you know.

Find the value of each of the following sums. Show your reasoning. Use number lines if you find them helpful.

1. \(\frac{1}{10} + \frac{3}{100}\)

   

   

2. \(\frac{24}{100} + \frac{4}{10}\)

   

   

3. \(\frac{7}{10} + \frac{13}{100}\)

   

   

Is the value of each expression greater than, less than or equal to 1? Explain how you know.

1. \(\frac{3}{10} + \frac{7}{100}\)
2. \(\frac{13}{10} + \frac{7}{100}\)
3. \(\frac{30}{100} + \frac{7}{10}\)

A chocolate cake recipe calls for 2 cups of flour. You gather your measuring cups and notice you have these sizes: \(\frac{1}{2}\) cup, \(\frac{1}{3}\) cup, \(\frac{1}{4}\) cup, and \(\frac{1}{6}\) cup.

1. What are the different ways you could use all 4 measuring cups to measure 2 cups of flour?
2. What are other ways you could use just some of the 4 measuring cups to measure exactly 2 cups of flour?

A dime is worth \(\frac{1}{10}\) of a dollar and a penny is worth \(\frac{1}{100}\) of a dollar. 

1. If I have \(\frac{89}{100}\) of a dollar, how many different combinations of dimes and pennies could I have? Use equations to show your reasoning.
2. A nickel is worth \(\frac{5}{100}\) of a dollar. How many different combinations of dimes, nickels and pennies could I have if I still have \(\frac{89}{100}\) of a dollar? Use equations to show your reasoning.