5B Cumulative Review 5 — Full Semester

A tank is divided into 1,000 equal units. Seven units are filled. Write the fraction and decimal of the whole that are filled; explain their equivalence.

Write 4.006 in words and in expanded decimal form. Identify the zero placeholders.

Which is greater, 2.307 or 2.37? Align the place values and explain.

Round 7.285 to the nearest hundredth and mark the two bounding hundredths and midpoint on a number line.

Compute 0.047 × 1,000. Explain the answer by counting thousandth units.

Calculate 75.6 ÷ 1,000. Show the corresponding exchange into smaller place-value units.

Convert 2.36 m to centimeters. Explain what happens to the unit count.

Calculate 4.95 + 3.70 mentally using a compensation strategy. State the exact answer.

Add 3.785 L and 0.679 L. Show how hundredths and thousandths regroup.

Subtract 7.386 from 20.000. Show an exchange across zero positions.

Compute 6.4 × 0.01. Explain why the product is smaller than 6.4.

Find 1.2 × 0.35 with a decomposition or area model. Explain the position of the decimal.

A jug holds 8.64 L. Divide it equally into four bottles. Find liters per bottle and verify by multiplication.

Divide 5.005 by 5, showing why the zero in the quotient matters.

How many groups of 0.1 are in 7? Draw or explain tenths and calculate.

Calculate 3 ÷ 0.25 and interpret the answer as a number of quarter-unit groups.

Using a ruler and protractor, draw an angle of 65°. Label its vertex and two rays; state its classification.

Two straight lines intersect. One angle measures 73°. Find its vertically opposite and an adjacent angle; explain both relationships.

A triangle has interior angles 110°, 35°, and 35°. Classify it by side family and angle family; explain using the equal angles.

A triangle has interior angles 49° and 64°. Find the third angle and explain the whole-angle total.

The two nonadjacent interior angles of a triangle are 47° and 68°. Find the exterior angle and explain why their sum works.

Explain why every rectangle is a parallelogram. Give an example of a parallelogram that is not a rectangle.

Three interior angles of a quadrilateral are 80°, 110° and 95°. Find the fourth; explain using triangles.

One angle of a parallelogram is 68°. Find the other three angles and give the parallel-line reasons.

Construct a triangle with adjacent sides 4 cm and 5 cm and included angle 60°. Describe how to verify it.

Four baskets contain 4, 5, 8 and 11 apples. Calculate the mean number of apples per basket and interpret it as a fair share.

Five boxes average 12 objects. Four contain 9, 11, 13 and 15. Find the fifth count and show total-first reasoning.

Draw a line plot of reading hours: 1,1,2,2,2,2,3,3,3. Identify the median and explain the position.

Plot A(1,2), B(4,2), and C(4,5) on a first-quadrant grid. Determine whether angle ABC is a right angle. Explain using the plotted coordinate changes.

A line passes through (0,4), (2,10), and (4,16). State the rule for y in terms of x and explain the change for each 1 step in x.

There are 12 red tokens and 18 blue tokens. Give the simplified ratio red:blue and explain why order matters.

Simplify 8:12 and show that 10:15 is equivalent by comparing common multipliers.

Two kinds of beads are in ratio 3:5, with 64 beads total. Find both counts using ratio units.

If a:b=2:3 and b:c=6:5, find a:b:c using one consistent value for b.

A container holds orange:white marbles in ratio 2:5, 56 total. Find orange and white counts and check their sum.

A bus travels 156 km in 3 hours at a constant rate. Find the rate and write its correct compound unit.

Notebooks cost $4.50 each. Find the cost of seven notebooks and name which quantity is the rate.

A runner covers 600 m in 2 minutes. Find meters per minute, then predict the distance in 4 minutes at the same rate.

A bus travels at 48 km/h for 2.5 hours. Find its distance, showing why the time and rate units work.

A 100-square grid has 36 shaded squares. What percentage is shaded, and what is the explicitly identified whole?

Convert 35% to a fraction in simplest terms. Explain what 100% represents.

Convert 0.075 to a percentage. Explain why a factor of 100 is used.

Convert 3/8 to a percentage, showing a fraction-to-decimal step.

Find 15% of 240 objects. Name the original whole before calculating.

A $80 jacket is discounted by 25%. Find the discount and final sale price; identify the original price as the percentage base.

Two runners recorded 4.086 km and 4.109 km. Which is farther, and what is the shorter result rounded to the nearest hundredth? Explain both decisions.

A ribbon is 0.375 m long. A roll contains 100 such lengths. Express the roll length in meters and centimeters.

A class divides 56.7 equally among 100 boxes, then adds 0.033 to each result. Calculate one final amount and give a mental-check strategy.

Three tanks contain 2.475 L, 1.608 L and 0.917 L. Together they are shared into two equal containers. How much is in each? Show an intermediate total.

A rectangle has sides 0.8 m and 0.35 m. Its area is reduced to one tenth of its original value. Find both areas and explain the scaling.

A craft shop has 5 m of tape and cuts 0.25 m pieces, then groups the pieces in packets of 10. How many full packets?

In a triangle, one angle is 64°. An exterior angle at another vertex is 120°. Find the other two interior angles, giving reasons.

A quadrilateral is split by a diagonal into two triangles. Explain its interior-angle total, then find the last angle if the others are 65°, 105° and 120°.

Describe how to construct a 5 cm by 3 cm rectangle and verify both its quadrilateral family and its four right angles.

Measurements are 3,3,5,7,7. Draw a line plot with X marks and calculate the mean; explain why the mode is not unique.

A straight-line reading has values 2,4,6,8 at hours 0,1,2,3. Find the mean value of these four readings and the rule y in terms of hour x.

Blue:red tokens are in ratio 5:3. There are 40 blue tokens. Find red tokens and total tokens; explain the part size.

In a three-color set, red:blue=2:3 and blue:green=6:5. There are 30 green items. Find red and blue counts.

A pump delivers 0.75 L every 15 seconds. At the same rate, how many liters arrive in 2 minutes? Show time conversion.

An $80 item is discounted by 15%, then a $4 coupon is applied. Find the amount paid, identifying which price the 15% uses.