My child knows 6 × 7 = 42. Why do they get stuck on 42 ÷ 6?

If your child knows 6 × 7 = 42 but gets stuck on 42 ÷ 6, they most likely learned the fact as a one-way answer. Division feels like a brand-new fact, even though it's the same one asked backwards. The fix is to connect them: say the whole fact family together, and ask each division as a times question.

Why a known fact suddenly looks new

When a child practices multiplication, the question always comes in the same shape: two numbers go in, one answer comes out. Six and seven go in, 42 comes out. After enough practice that path is quick and sure.

Division asks for the trip in the other direction. Now 42 goes in, and your child has to find the missing piece. If they've only ever traveled from 6 and 7 to 42, nothing about 42 ÷ 6 points them back. So they start over: counting by sixes, guessing, or looking at you for a hint.

The answer they need is already in their head. They just haven't learned that it answers this question too.

What a fact family is

A fact family is the small group of facts made from the same three numbers. For 6, 7 and 42, it looks like this:

• 6 × 7 = 42
• 7 × 6 = 42
• 42 ÷ 6 = 7
• 42 ÷ 7 = 6

Four facts, one set of numbers. When a child sees them side by side, division stops looking like a separate subject. It's the same fact viewed from another side.

What to do tonight

Start with facts they already know well

Pick two or three multiplication facts your child answers straight away, without counting. This matters. If the times fact itself is shaky, the division built on it will be shaky too. Save the harder facts for later and use the easy wins to learn the connection.

Say the family together

Write the three numbers on a scrap of paper, or just say them: 6, 7 and 42. Then say the family out loud together, all four facts, slowly. Let your child point to each number as you say it. Do this once or twice. You're showing them that one set of numbers makes four true sentences.

Ask the division as a times question

Now ask, "What's 42 divided by 6?" If they hesitate, turn it around for them: "6 times what makes 42?" Most children find the answer right away when the question is shaped like the facts they know.

After a few tries, pause before offering the hint. Give them a moment to do the turning around on their own. That quiet step, "42 ÷ 6 means 6 times what is 42," is the whole skill.

A few at a time, and stop while it's going well

Two or three fact families in one evening is enough. End after a division they answered on their own, even if it was an easy one. A good finish makes it more likely they'll want to try again.

How you'll know it's working

At first you'll hear your child talking it through: "six times... seven. It's seven." That's a good sign. They're reaching for the times fact instead of counting up from zero.

Over time the pause gets shorter, and the spoken step drops away. You may also notice them turning division questions into times questions on their own, in homework or a worksheet, without being asked. When that happens with the easy families, add one new family built from a fact they've just become sure of.

A calm way to practice

A child who knows 6 × 7 has already done most of the work for 42 ÷ 6. Showing them the fact family lets that work count twice.

For quick practice with the times facts that division depends on, try Flash Cards for free.

When you're ready for more practice later, Founding Scholar adds Extra Practice.