Use properties of operations to scale recipes for a school event.
Scale the Recipes
A bakery is preparing food for a school event. Rewrite each expression without changing its value. Variables represent nonnegative quantities.
1.
One batch uses x cups of whole-wheat flour and 2 cups of white flour. Complete the expanded expression for 5 batches.
5(x + 2) = x +
2.
A muffin batch needs 2x scoops of oats and 3 scoops of seeds. Which expression is equivalent to 4(2x + 3), the scoops needed for 4 batches?
3.
A revised recipe uses x − 1/4 cup of oil per batch, where x is at least 1/4. Expand the expression for 6 batches.
6(x − 1/4) = x −
4.
The expression 0.5(6 + x) gives the cups of fruit needed for a half batch. Which expression has the same value for every x?
5.
Match each recipe-scaling expression to its equivalent expanded expression.
Organize the Batch Totals
Use properties of operations to reorder, regroup, combine, or factor expressions.
6.
The bakery records scoops of oats as (8 + x) + 5. Which rewrite uses only the associative property of addition, changing the grouping but not the order?
7.
There are 2 racks, with 7 trays on each rack and x rolls on each tray. Regroup the factors to simplify.
2(7x) = (2 × 7)x = x
8.
The bakery combines two flour totals: 3x + 4 + 5x + 2. Which expression is equivalent after combining like terms?
9.
The fruit needed for two sets of half batches is 1/2 × x + 1/2 × x cups. Combine the like terms.
1/2 × x + 1/2 × x = x
10.
A recipe total is 18x + 30. Factor out the greatest whole-number factor shared by 18 and 30.
18x + 30 = (x + )
Check the Event Plan
Apply equivalent expressions to the bakery's plans. Explain your reasoning in the final question.
11.
Each breakfast box contains x plain rolls and 2 seeded rolls. The bakery fills 9 boxes, then adds 3x extra plain rolls to a serving basket. Which simplified expression gives the total number of rolls?
12.
The bakery makes 4 batches of oat bars and 4 batches of fruit bars. Each oat-bar batch needs x cups of oats, and each fruit-bar batch needs 1.5 cups of oats. Which factored expression gives the total cups of oats?
13.
Each of 3 pastry trays contains 2x berry pastries and 4 apple pastries. Select all expressions that give the total number of pastries on the 3 trays for every x.
14.
Amira and Jon both factor the flour total 12x + 18 for a biscuit order. Amira writes 2(6x + 9), and Jon writes 6(2x + 3). Are both expressions equivalent to 12x + 18? Which one uses the greatest common factor? Explain using the distributive property.