Grade 6 · Build equivalent batches · 102 of 750
Build equivalent batches · practice 11
One batch has 3 units of A and 2 units of B. Find both quantities in 6 identical batches and the fraction of the total that is A. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
Learn with Amar Video lesson · 26 sec
Ratios: scale both quantities
AI-assisted presenter with an American male AI voice. Scale a 3:2 ratio by six to get 18:12, then compare the 18 blue counters with all 30 counters to find a fraction of 3/5.
Read the full transcript
One batch contains three blue counters and two orange counters. Make six identical batches. Blue becomes eighteen, and orange becomes twelve. Both quantities multiplied by six, so the ratio stays three to two. Of all thirty counters, eighteen are blue: three fifths of the total.
01 · Make a prediction
Your practice question
One batch has 3 units of A and 2 units of B. Find both quantities in 6 identical batches and the fraction of the total that is A.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Multiply both batch amounts by the same batch count.
Work through the reasoning
Step 1
Translate the givens
One batch totals 3 + 2 = 5 units. Its ordered ratio A:B is 3:2.
Step 2
Calculate with the model
6 batches contain A = 3 × 6 = 18 and B = 2 × 6 = 12.
Step 3
Check and interpret
The total is 30. The A fraction is 18/30 = 3/5; the batch count cancels.
The answer
A = 18; B = 12; A's share = 3/5.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
The mathematical idea
Equivalent ratios multiply both quantities by the same factor. Building complete copies makes that requirement visible: multiplying just one quantity changes the mixture. A part-to-part ratio is different from either part as a fraction of the combined total. Starting quantities: First quantity per batch = 3; Second quantity per batch = 2; Final complete batches = 6.
a : b = ka : kb
03 · Reflect and transfer
Explain what changes and why.
How does a part-to-part ratio differ from a part-to-whole fraction?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.