---
id: 5900f3b31000cf542c50fec6
title: 'Problem 71: Ordered fractions'
challengeType: 5
forumTopicId: 302184
dashedName: problem-71-ordered-fractions
---

# --description--

Consider the fraction, `n`/`d`, where `n` and `d` are positive integers. If `n`<`d` and HCF(`n`,`d`)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for `d` ≤ 8 in ascending order of size, we get:

<div style='text-align: center;'>1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, <strong>2/5</strong>, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8</div>

It can be seen that 2/5 is the fraction immediately to the left of 3/7.

By listing the set of reduced proper fractions for `d` ≤ 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7.

# --hints--

`orderedFractions()` should return a number.

```js
assert(typeof orderedFractions() === 'number');
```

`orderedFractions()` should return 428570.

```js
assert.strictEqual(orderedFractions(), 428570);
```

# --seed--

## --seed-contents--

```js
function orderedFractions() {

  return true;
}

orderedFractions();
```

# --solutions--

```js
// solution required
```