Event Bakery: Recipe Balancing

Use properties of operations to combine recipe adjustments efficiently.

Recipe Checks

A bakery is scaling recipes for a school event. Positive adjustments add an ingredient; negative adjustments reduce it. Use helpful groups rather than calculating only from left to right.

A scaled muffin recipe needs 6 3/8 cups of flour. The baker reduces it by 1 5/8 cups. Split the reduction into 3/8 cup and another amount to reach a whole number first.

6 3/8 − 1 5/8 = (6 3/8 − 3/8) −

Two test adjustments to a bread recipe are +3/4 cup and −1/2 cup. The baker decides not to use either adjustment. Which expression removes their combined effect from a planned 8 cups?

A. 8 + 3/4 + (−1/2)B. 8 + (−3/4) + 1/2C. 8 + 3/4 + 1/2D. 8 − 3/4 − 1/2

A cookie recipe's butter adjustments are −1 3/4 cups and +5/8 cup. Break −1 3/4 into −1 and −3/4, then combine the fractional parts. Write the total as a fraction or mixed number.

Total signed adjustment: cups

A scaled glaze recipe needs 7.25 kg of sugar before a reduction of 2.98 kg. Which rewrite makes the subtraction easier without changing the result?

A. Use 7.25 − 3 + 0.98.B. Use 7.25 − 2 + 0.98.C. Use 7.25 − 3 + 0.02.D. Use 7.25 − 3 − 0.02.

The baker checks 5/6 − (1/3 + 1/4) cup of oil. Select every expression equivalent to this calculation.

Combine Batch Plans

The amounts below have already been scaled. Combine or compare them using addition and subtraction properties.

The bakery combines the sugar adjustments for four recipes. Group amounts that make whole numbers.

Sugar Adjustments
Recipe	Change (kg)
Oat cookies	+1.35
Lemon loaves	−0.45
Spice muffins	+0.65
Cocoa squares	−0.55

What is the total signed sugar adjustment? kg

The flour estimate is 9 1/2 + 4 3/4 − 3 1/2 cups. Which rewrite uses addition properties to group terms with matching fractional parts?

A. (9 1/2 + 3 1/2) + 4 3/4B. 9 1/2 − (4 3/4 + 3 1/2)C. (9 1/2 + (−4 3/4)) + 3 1/2D. (9 1/2 + (−3 1/2)) + 4 3/4

One plan uses 4 7/8 cups of milk for bread and 2 1/3 cups for muffins. A second plan uses 4 3/8 cups for bread and the same 2 1/3 cups for muffins. Cancel the shared amount when comparing the totals.

How much more milk does the first plan use? cup

The bakery has 18.75 kg of flour. It sets aside 4.6 kg for bread and 3.4 kg for rolls, then receives 1.25 kg more. Group the two amounts set aside and group the starting amount with the delivery.

How much flour remains available? kg

10.

For any planned amount x, a baker adds 2/5 cup and then removes 2/5 cup. Which statement correctly explains why x + (2/5 + (−2/5)) = x?

A. The opposite adjustments sum to zero, and adding zero preserves x.B. The two adjustments are equal, so their sum must equal x.C. The opposite adjustments sum to one, and adding one preserves x.D. The two adjustments cancel x, so the whole expression equals zero.

Audit the Final Recipes

Check that each shortcut preserves the value of the original calculation. Write fraction answers in simplest form.

11.

A dough recipe's signed water adjustment is −7/12 + 1/4 + 1/3 cup. Combine the two positive fractions first.

What is the total signed adjustment? cups

12.

A baker uses the equivalent calculation 6.48 − 2.75 = 6.73 − 3 to check an ingredient amount. Why is this valid?

A. Adding 0.25 to both numbers leaves their difference unchanged.B. Adding 0.25 to both numbers decreases their difference by 0.25.C. Adding 0.25 to both numbers makes their difference equal zero.D. Adding 0.25 to both numbers increases their difference by 0.50.

13.

A scaled batter starts with 3 5/6 cups of milk. The baker applies one group's net adjustment of (−2/3 + 1/6) cup, then subtracts another group's net adjustment of (1/4 − 3/4) cup. Simplify each group before combining.

3 5/6 + (−2/3 + 1/6) − (1/4 − 3/4) = cups

14.

A recipe check is 4 1/2 − (3/4 + (−1/4)) cups. Mateo rewrites it as 4 1/2 − 3/4 − 1/4 because he thinks removing parentheses means subtracting both positive fraction amounts. Explain what happens to each sign when the grouped sum is subtracted. Give a correct rewrite and the final amount.